QB

1. Define Sampling Theorem.

1.​ Sampling theorem states that a continuous-time signal can be perfectly reconstructed
if sampled at a rate greater than twice its highest frequency component
2.​ Mathematically expressed as fs > 2fmax, where fs is sampling frequency and fmax is
highest frequency
3.​ Ensures no information loss during analog-to-digital conversion
4.​ Forms the fundamental basis for digital signal processing

2. What is Nyquist rate?

1.​ Nyquist rate is the minimum sampling rate required to reconstruct a signal without
aliasing
2.​ Equal to exactly twice the highest frequency component in the signal (2fmax)
3.​ Represents the theoretical boundary between adequate and inadequate sampling
4.​ Critical parameter in ADC design and digital communication systems

3. Define aliasing in signal processing.

1.​ Aliasing is the distortion that occurs when a signal is sampled below the Nyquist rate
2.​ Results in higher frequencies appearing as lower frequencies in the reconstructed
signal
3.​ Creates incorrect representation of the original signal that cannot be corrected
4.​ Causes irreversible information loss in the sampling process

4. What is Quantization Error?

1.​ Quantization error is the difference between actual analog value and its quantized
digital representation
2.​ Occurs during analog-to-digital conversion due to finite precision
3.​ Manifests as quantization noise in the reconstructed signal
4.​ Decreases as the number of quantization levels increases

5. Define Pulse Code Modulation (PCM).

1.​ PCM is a digital modulation technique that converts analog signals to digital by
sampling, quantizing, and encoding
2.​ Uses uniform time intervals for sampling and discrete amplitude levels for
quantization
3.​ Represents each sample as a binary coded word
4.​ Forms the basis for most digital audio and telephony systems
6. What is Delta Modulation?
1.​ Delta Modulation is a simplified form of differential PCM that encodes only the
difference between consecutive samples
2.​ Uses only one bit per sample to indicate whether the signal increased or decreased
3.​ Simpler implementation but less accurate than PCM, especially for rapidly changing
signals
4.​ Requires higher sampling rates to achieve acceptable performance

7. Differentiate between uniform and non-uniform

quantization.
1.​ Uniform quantization: Equal step sizes between quantization levels; simpler
implementation but less efficient for signals with varying amplitudes
2.​ Non-uniform quantization: Varying step sizes; smaller steps for commonly occurring
amplitudes and larger steps for rare amplitudes
3.​ Non-uniform provides better SNR for signals with non-uniform probability distribution
(like speech)
4.​ Non-uniform is typically implemented using companding (compression-expansion)
techniques like μ-law or A-law

8. Derive the Nyquist rate and discuss its significance.

1.​ For a bandlimited signal x(t) with highest frequency fmax, the Fourier transform X(f) =
0 for |f| > fmax
2.​ When sampling at rate fs, the spectrum repeats at intervals of fs, requiring fs/2 >
fmax to avoid overlap
3.​ Therefore, Nyquist rate = 2fmax is the minimum sampling frequency to avoid aliasing
4.​ Significance: Defines fundamental limit for perfect signal reconstruction; enables
efficient digitization with minimum samples

9. Explain the concept of Sampling Theorem with an

example.
1.​ Sampling theorem states that a bandlimited signal can be perfectly reconstructed if
sampled above twice its highest frequency
2.​ Example: For voice signal with highest frequency of 4 kHz, sampling rate must
exceed 8 kHz
3.​ Telephone systems use 8 kHz sampling rate, allowing reconstruction of signals up to
4 kHz
4.​ When sampling below Nyquist rate (e.g., 6 kHz for a 4 kHz signal), frequencies
above 3 kHz would alias and distort the signal
10. Explain aliasing and how it affects digital
communication.
1.​ Aliasing occurs when sampling rate is below Nyquist rate, causing high frequencies
to appear as lower frequencies
2.​ In digital communication, aliasing causes irreversible signal distortion and
interference
3.​ Can lead to increased bit error rates, loss of information, and degraded quality of
service
4.​ Prevented by using anti-aliasing filters to limit input signal bandwidth before sampling

11. Describe Quantization Error and methods to reduce

it.
1.​ Quantization error is the difference between actual analog value and nearest
quantization level
2.​ Methods to reduce: Increase number of quantization levels (bits per sample)
3.​ Use non-uniform quantization (companding) to allocate more levels to commonly
occurring amplitudes
4.​ Implement dithering techniques to randomize error and convert distortion to less
objectionable noise

12. Explain Pulse Code Modulation (PCM) with a block

diagram.
1.​ Input stage: Bandlimited analog signal passes through anti-aliasing filter
2.​ Sampling stage: Signal is sampled at regular intervals above Nyquist rate
3.​ Quantization stage: Samples are approximated to nearest quantization level
4.​ Encoding stage: Quantized values are converted to binary code words for
transmission

13. Compare PCM and Delta Modulation with

advantages and disadvantages.
PCM advantages:

1.​ Higher accuracy and signal quality

2.​ Better noise immunity at reasonable bit rates
3.​ Well-established standards and implementations
4.​ Suitable for various signal types

Delta Modulation advantages:

1.​ Simpler hardware implementation

 2.​ Lower bandwidth requirements for slowly varying signals
3.​ Lower complexity encoding and decoding
4.​ Natural compression for certain signals

14. Explain Quantization Error in PCM and methods to

reduce it.
1.​ Quantization error in PCM is the difference between actual sample value and
quantized value
2.​ Modeled as additive noise with uniform distribution between ±Δ/2 (Δ = step size)
3.​ SNR improves by approximately 6 dB for each additional bit of quantization
4.​ Methods to reduce: Increase quantization bits, implement non-uniform quantization,
use adaptive quantization

15. Derive the expression for Signal-to-Noise Ratio

(SNR) in PCM.
1.​ For uniform quantization with step size Δ, quantization noise power σ²q = Δ²/12
2.​ For a sinusoidal signal with amplitude A, signal power σ²s = A²/2
3.​ SNR = σ²s/σ²q = (3/2)·(2²ᵇ), where b is number of quantization bits
4.​ In dB: SNR = 10log₁₀(3/2) + 20log₁₀(2ᵇ) ≈ 1.76 + 6.02b dB

16. Explain the Sampling Theorem and derive its

mathematical expression.
1.​ Sampling theorem states that x(t) with X(f)=0 for |f|>fmax can be perfectly
reconstructed if sampled above 2fmax
2.​ Sampled signal: xs(t) = x(t)·∑δ(t-nTs) where Ts=1/fs is sampling period
3.​ Frequency domain: Xs(f) = (1/Ts)·∑X(f-nfs), showing spectrum repeats at intervals fs
4.​ Perfect reconstruction requires fs>2fmax to avoid overlap between repeated spectra

17. Discuss the significance of Nyquist rate in

preventing aliasing.
1.​ Nyquist rate (2fmax) represents the minimum sampling frequency to prevent aliasing
2.​ Sampling below Nyquist rate causes spectrum overlap, making separation
impossible
3.​ Establishing Nyquist rate correctly allows proper anti-aliasing filter design
4.​ Ensures information preservation and enables perfect signal reconstruction

18. Compare the advantages and disadvantages of

PCM and Delta Modulation.
PCM advantages:

1.​ Better accuracy and lower noise sensitivity

2.​ Maintains quality over multiple encoding/decoding cycles
3.​ Standards-based implementation across industries
4.​ Suitable for complex signals with rapid amplitude changes

Delta Modulation disadvantages:

1.​ Suffers from slope overload distortion for rapidly changing signals
2.​ Higher sampling rates required for comparable quality
3.​ Accumulates errors over time due to integration
4.​ Limited dynamic range without adaptive implementations

19. Explain different types of pulse modulation

techniques with examples.
1.​ Pulse Amplitude Modulation (PAM): Sample amplitude directly represents signal
(e.g., computer sound cards)
2.​ Pulse Width Modulation (PWM): Pulse width varies proportionally to sample
amplitude (e.g., motor control)
3.​ Pulse Position Modulation (PPM): Pulse position varies with signal amplitude (e.g.,
optical communications)
4.​ Pulse Code Modulation (PCM): Sample quantized and encoded as binary (e.g.,
digital telephony, audio CDs)

20. Describe the process of Analog to Digital

conversion using PCM.
1.​ Anti-aliasing filtering: Limit input signal bandwidth to prevent aliasing
2.​ Sampling: Convert continuous-time signal to discrete-time using sample-and-hold
circuit
3.​ Quantization: Approximate sample amplitudes to nearest quantization levels
4.​ Encoding: Convert quantized values to digital code words (typically binary)

21. Explain the concept of companding and its

importance in digital communication.
1.​ Companding combines compression at transmitter and expansion at receiver
2.​ Applies non-uniform quantization using logarithmic scales like μ-law or A-law
3.​ Reduces quantization noise for low-amplitude signals while maintaining acceptable
SNR
4.​ Critical for voice communications to accommodate wide dynamic range with limited
bits
22. Define digital modulation.
1.​ Digital modulation is the process of encoding digital information onto an analog
carrier wave
2.​ Changes carrier parameters (amplitude, frequency, phase) based on digital input
3.​ Enables transmission of digital data over analog channels such as wireless media
4.​ Basic types include ASK, FSK, PSK, and combinations like QAM

23. What is BASK, and how does it work?

1.​ Binary Amplitude Shift Keying (BASK) represents digital bits by varying carrier
amplitude
2.​ Typically, bit '1' represented by presence of carrier, bit '0' by absence or reduced
amplitude
3.​ Simplest form is On-Off Keying (OOK), where carrier is either on or off
4.​ Mathematically: s(t) = A·m(t)·cos(2πfct), where m(t) is the binary message

24. Explain the principle of BPSK.

1.​ Binary Phase Shift Keying (BPSK) encodes data by shifting carrier phase between
two values
2.​ Typically 0° for bit '1' and 180° for bit '0', creating two opposite phases
3.​ Mathematically: s(t) = A·cos(2πfct + π·m(t)), where m(t) is 0 or 1
4.​ Offers better noise immunity than BASK with same bandwidth requirement

25. How does BFSK differ from BPSK?

1.​ Binary Frequency Shift Keying (BFSK) modulates carrier frequency rather than
phase
2.​ Uses two distinct frequencies to represent bits (f₁ for '0', f₂ for '1')
3.​ Mathematically: s(t) = A·cos(2π(fc+m(t)·Δf)t), where Δf is frequency deviation
4.​ Simpler to implement but requires more bandwidth than BPSK for the same bit rate

26. What is the role of coherent detection in digital

modulation?
1.​ Coherent detection uses local oscillator synchronized in phase with received carrier
2.​ Enables optimal detection by maximizing signal-to-noise ratio
3.​ Allows for lower error rates compared to non-coherent detection
4.​ Requires more complex receiver design with phase recovery circuits

27. What are M-ary transmission techniques?

1.​ M-ary techniques use multiple (M>2) signal levels to represent digital information
 2.​ Each symbol carries log₂(M) bits, increasing spectral efficiency
3.​ Examples include M-PSK, M-QAM, M-FSK with M different states
4.​ Trade higher spectral efficiency for increased power requirements and complexity

28. Compare coherent and non-coherent reception.

1.​ Coherent reception requires carrier phase synchronization; non-coherent does not
2.​ Coherent offers better performance (lower BER) but requires more complex circuitry
3.​ Non-coherent is simpler to implement but requires higher SNR for same error
performance
4.​ Coherent is preferred for PSK; non-coherent is often used for FSK

29. Explain the working principle of BASK and its

practical applications.
1.​ BASK modulates carrier amplitude proportional to binary signal (presence/absence of
carrier)
2.​ Simple implementation using product modulator and envelope detector
3.​ Applications: RFID systems, optical fiber communications, infrared remote controls
4.​ Limited performance in noisy environments due to amplitude sensitivity

30. Compare the advantages and disadvantages of

coherent and non-coherent detection.
Coherent advantages:

1.​ Better noise immunity and lower bit error rates

2.​ More efficient use of transmitter power
3.​ Enables more complex modulation schemes
4.​ Better performance in fading channels

Non-coherent advantages:

1.​ Simpler receiver implementation

2.​ No need for carrier recovery circuits
3.​ Better performance when phase is rapidly changing
4.​ Lower cost and power consumption

31. How does increasing M-ary levels impact spectral

efficiency and power efficiency?
1.​ Spectral efficiency increases logarithmically with M as each symbol carries log₂(M)
bits
2.​ Bandwidth efficiency improves as more bits are transmitted per symbol period
 3.​ Power efficiency decreases as M increases due to reduced distance between
constellation points
4.​ Higher M requires approximately 6 dB more power for each doubling of symbols to
maintain same error rate

32. Explain the role of probability of error in digital

communication systems.
1.​ Probability of error (Pe) quantifies system reliability and performance
2.​ Determines the trade-off between power efficiency, bandwidth, and data integrity
3.​ Used to calculate bit error rate (BER) for comparing different modulation schemes
4.​ Guides system design choices including modulation type, coding, and power
requirements

33. Discuss the impact of noise on different digital

modulation techniques.
1.​ BASK: Most vulnerable to noise due to amplitude sensitivity; requires highest SNR
2.​ BPSK: Better noise immunity; requires 3-6 dB less power than BASK for same error
rate
3.​ BFSK: Performance between BASK and BPSK; more robust to non-linear distortions
4.​ QAM: Higher order QAM schemes increasingly susceptible to noise as constellation
density increases

34. Explain how channel coding enhances the

performance of digital modulation schemes.
1.​ Channel coding adds controlled redundancy to detect and correct errors
2.​ Reduces required SNR for given BER, known as coding gain
3.​ Improves system performance in fading channels through time diversity
4.​ Enables operation closer to Shannon capacity limit for more efficient spectrum use

35. Explain the working principle of BASK with

mathematical expressions and waveforms.
1.​ BASK signal s(t) = A·m(t)·cos(2πfct), where m(t) is 0 or 1
2.​ For bit '1': s₁(t) = A·cos(2πfct); For bit '0': s₀(t) = 0 or reduced amplitude
3.​ Signal constellation consists of two points along real axis at 0 and A
4.​ Demodulation uses envelope detection or coherent product detection

36. Derive the probability of error for BFSK and explain

its significance.
 1.​ For coherent BFSK: Pe = 0.5·erfc(√(Eb/N₀))
2.​ For noncoherent BFSK: Pe = 0.5·exp(-Eb/2N₀)
3.​ BFSK requires ~3dB more power than BPSK for same error performance
4.​ Significance: Allows system designers to calculate required transmit power for target
reliability

37. Analyze the effect of increasing M-ary levels on

bandwidth and error probability.
1.​ Bandwidth efficiency increases by factor log₂(M) compared to binary systems
2.​ For same energy per bit, symbol error probability increases with M
3.​ Minimum distance between constellation points decreases as dmin ∝ 1/√M
4.​ Required SNR increases ~3dB for each doubling of M to maintain same symbol error
rate

38. Derive the bit error rate (BER) expressions for

BPSK and BFSK and compare their performance.
BPSK:

1.​ BER = 0.5·erfc(√(Eb/N₀))

2.​ Offers best power efficiency among basic modulation schemes

BFSK: 3. Coherent BER = 0.5·erfc(√(Eb/2N₀)) 4. BPSK outperforms BFSK by ~3dB in power

efficiency for same BER

39. Compare coherent and non-coherent detection in

terms of performance and complexity.
Performance:

1.​ Coherent detection achieves ~3dB better SNR performance

2.​ Non-coherent detection suffers more in multipath environments

Complexity: 3. Coherent requires carrier recovery circuits and phase-locked loops 4.

Non-coherent uses simpler envelope or differentially coherent detection

40. Discuss the trade-offs between spectral efficiency

and power efficiency in digital modulation techniques.
1.​ Higher spectral efficiency (bits/Hz) typically requires higher order modulation (larger
M)
2.​ Power efficiency decreases with higher spectral efficiency (Shannon limit constraint)
3.​ Power-efficient schemes (BPSK, QPSK) have lower spectral efficiency
 4.​ Spectrally efficient schemes (16-QAM, 64-QAM) require higher power for reliable
transmission

41. Explain the impact of noise on digital modulation

techniques and suggest ways to mitigate it.
Impact:

1.​ Adds random variations to signal constellation points

2.​ Increases probability of symbol misidentification
3.​ Higher order modulations more susceptible to noise effects

Mitigation methods: 4. Forward error correction coding, adaptive modulation, equalization,

diversity techniques

42. Explain the concept of constellation diagrams and

how they are used in digital modulation.
1.​ Constellation diagrams are 2D representations of modulated signals in I/Q plane
2.​ Points represent possible symbol states; axes represent in-phase and quadrature
components
3.​ Used to visualize decision boundaries, signal space coverage, and modulation
efficiency
4.​ Enable analysis of system performance, including effects of noise, phase jitter, and
distortion

43. A source produces 4 symbols with probabilities 1/2,

1/4, 1/8, and 1/8. Find the information content of each
symbol.
1.​ Information content I(x) = -log₂(p(x)) where p(x) is symbol probability
2.​ Symbol 1: I(x₁) = -log₂(1/2) = 1 bit
3.​ Symbol 2: I(x₂) = -log₂(1/4) = 2 bits
4.​ Symbols 3 and 4: I(x₃) = I(x₄) = -log₂(1/8) = 3 bits each

44. Define entropy in the context of information theory.

1.​ Entropy is the average information content of symbols from a source
2.​ Mathematically: H(X) = -∑p(x)log₂(p(x)) for all symbols x
3.​ Represents the minimum number of bits needed on average to encode source
symbols
4.​ Measures uncertainty or randomness of an information source
45. What is the significance of the Shannon-Hartley
Capacity Theorem?
1.​ Defines theoretical maximum data rate (C) for reliable communication over noisy
channel
2.​ C = B·log₂(1+S/N), where B is bandwidth, S/N is signal-to-noise ratio
3.​ Establishes fundamental limit that cannot be exceeded regardless of coding scheme
4.​ Guides design of practical communication systems to approach theoretical efficiency

46. Explain the term 'Information Rate'.

1.​ Information rate is the amount of information transmitted per unit time
2.​ Measured in bits per second (bps) or related units
3.​ Calculated as R = H(X)·fs where H(X) is source entropy and fs is symbol rate
4.​ Upper bounded by channel capacity according to Shannon's theorem

47. How does channel capacity affect data

transmission?
1.​ Channel capacity sets theoretical maximum data rate for error-free transmission
2.​ Attempting to transmit above capacity guarantees errors regardless of coding
3.​ Approaching capacity requires increasingly complex coding schemes
4.​ Guides selection of modulation, coding rate, and bandwidth allocation

48. What are the key differences between

Shannon-Fano and Huffman encoding?
1.​ Shannon-Fano divides symbols into two groups based on cumulative probability
2.​ Huffman builds codes from bottom-up, combining lowest probability symbols first
3.​ Huffman always produces optimal prefix codes; Shannon-Fano may not be optimal
4.​ Huffman guarantees average code length within 1 bit of entropy; Shannon-Fano
doesn't

49. Define code efficiency and redundancy in source

coding.
1.​ Code efficiency (η) = H(X)/L, where H(X) is entropy and L is average code length
2.​ Measures how close a code comes to theoretical minimum length (100% = optimal)
3.​ Redundancy (r) = 1 - η = (L-H(X))/L
4.​ Represents fraction of bits that could theoretically be eliminated with optimal coding
50. Why is channel encoding necessary in digital
communication?
1.​ Detects and/or corrects errors caused by channel noise and interference
2.​ Improves reliability of transmission in adverse conditions
3.​ Enables operation closer to Shannon capacity limit
4.​ Compensates for channel impairments like fading, multipath, and burst errors

51. State entropy, its expression in a binary PCM

systems the binits 0 and 1 are transmitted. Calculate
the amount of information conveyed by the binits If
they are equally likely to be transmitted and unit.
1.​ Entropy H(X) = -∑p(x)log₂(p(x)) for all symbols x
2.​ In binary PCM with equally likely binits, p(0) = p(1) = 0.5
3.​ H(X) = -[0.5log₂(0.5) + 0.5log₂(0.5)] = -[0.5(-1) + 0.5(-1)] = 1 bit
4.​ Information conveyed by each binit is exactly 1 bit when equally likely

52. Four symbols of the alphabet of discrete memory

less source and their probabilities are given as
{S1,S2,S3,S4) and {1/3, 1/6, 1/4, 1/4}. Point out the
symbols using Shannon fano coding and calculate the
average code word length and efficiency.
Shannon-Fano codes:

1.​ S1 (1/3): 0, S2 (1/6): 10, S3 (1/4): 110, S4 (1/4): 111

2.​ Average code length: L = (1×1/3) + (2×1/6) + (3×1/4) + (3×1/4) = 1/3 + 1/3 + 3/4 + 3/4
= 2.167 bits
3.​ Entropy: H(X) = -[1/3·log₂(1/3) + 1/6·log₂(1/6) + 1/4·log₂(1/4) + 1/4·log₂(1/4)] = 1.915
bits
4.​ Efficiency: η = H(X)/L = 1.915/2.167 = 0.884 or 88.4%

53. Define Entropy and Information rate of Discrete

Memoryless source. Consider a DMS with a source
alphabet {S0, S1, S2} and source statistics {0.7, 0.15,
0.15}. Find: 1) Information content of each message. 2)
Entropy of DMS.
Definition:

1.​ Entropy is average information content: H(X) = -∑p(x)log₂(p(x))

2.​ Information rate is entropy multiplied by symbol rate: R = H(X)·rs

Information content: 3. I(S0) = -log₂(0.7) = 0.515 bits, I(S1) = I(S2) = -log₂(0.15) = 2.737 bits

Entropy: 4. H(X) = -[0.7·log₂(0.7) + 0.15·log₂(0.15) + 0.15·log₂(0.15)] = 0.7·0.515 +

0.15·2.737 + 0.15·2.737 = 1.093 bits

54. A source emits five messages with probabilities 1/3,

1/3, 1/9, 1/9, and 1/9 respectively. Encode using
Shanon-Fano Code. Find the entropy of the source and
compact binary code and also find the average length
of the codeword. Determine the efficiency and
redundancy of this code.
Shannon-Fano codes:

1.​ S1 (1/3): 00, S2 (1/3): 01, S3 (1/9): 100, S4 (1/9): 101, S5 (1/9): 11

Calculations: 2. Average length: L = 2·(1/3) + 2·(1/3) + 3·(1/9) + 3·(1/9) + 2·(1/9) = 2.222 bits
3. Entropy: H(X) = -[1/3·log₂(1/3) + 1/3·log₂(1/3) + 1/9·log₂(1/9)×3] = 2.113 bits 4. Efficiency: η
= H(X)/L = 2.113/2.222 = 0.951 or 95.1%; Redundancy: r = 1-η = 0.049 or 4.9%

55. Explain the concept of forward error correction.

1.​ Forward error correction (FEC) adds redundancy to transmitted data
2.​ Enables receiver to detect and correct errors without retransmission
3.​ Uses block codes (e.g., Hamming, BCH, Reed-Solomon) or convolutional codes
4.​ Improves reliability at expense of increased bandwidth or reduced data rate

56. What is Hamming Distance, and why is it

important?
1.​ Hamming distance is the number of bit positions in which two codewords differ
2.​ Minimum Hamming distance (dmin) determines error detection and correction
capability
3.​ A code with dmin can detect up to (dmin-1) errors and correct up to ⌊(dmin-1)/2⌋
errors
4.​ Important for designing and evaluating error correction codes
57. Differentiate between systematic and
non-systematic codes.
1.​ Systematic codes: Original data bits appear unchanged within codeword, followed by
parity bits
2.​ Non-systematic codes: Original data bits are not explicitly present in codeword
3.​ Systematic codes allow easier data extraction without full decoding
4.​ Non-systematic codes may offer better error correction performance but require
complete decoding

58. Explain the function of syndrome testing in error

detection.
1.​ Syndrome is calculated by multiplying received vector by parity check matrix
2.​ Zero syndrome indicates no errors detected; non-zero syndrome indicates errors
3.​ Syndrome pattern uniquely identifies error location in single-error-correcting codes
4.​ Enables efficient error detection and correction without comparing to all valid
codewords

59. What is a generator polynomial in cyclic codes?

1.​ Generator polynomial g(x) is a key defining element of cyclic codes
2.​ All valid codewords are multiples of the generator polynomial
3.​ Properties of g(x) determine error detection and correction capabilities
4.​ Degree of g(x) equals number of parity bits in systematic cyclic code

60. Describe the role of a feedback shift register in

polynomial division.
1.​ Implements division by generator polynomial in hardware-efficient manner
2.​ Performs multiplication, addition, and shift operations using registers and XOR gates
3.​ Used for both encoding (creating parity bits) and syndrome calculation (error
detection)
4.​ Enables real-time processing of cyclic codes with minimal computational complexity

61. Compare Shannon-Fano and Huffman encoding,

providing step-by-step examples.
Shannon-Fano:

1.​ Sort symbols by probability in decreasing order

2.​ Recursively divide list into two parts with approximately equal probability
3.​ Assign 0 to first group, 1 to second group; repeat subdivision
Huffman: 4. Build bottom-up by repeatedly combining two lowest probability symbols to form
new node

62. Explain Shannon's entropy equation and its

significance in data transmission.
1.​ H(X) = -∑p(x)log₂(p(x)) measures average information content of source
2.​ Sets theoretical minimum bits required to represent source without loss
3.​ Guides design of optimal source coding schemes
4.​ Lower bound for average code length in lossless compression

63. Calculate the entropy of a discrete information

source with the following probabilities: P(X=0) = 0.4,
P(X=1) = 0.3, P(X=2) = 0.2, P(X=3) = 0.1.
1.​ H(X) = -∑p(x)log₂(p(x))
2.​ H(X) = -[0.4·log₂(0.4) + 0.3·log₂(0.3) + 0.2·log₂(0.2) + 0.1·log₂(0.1)]
3.​ H(X) = -[0.4·(-1.32) + 0.3·(-1.74) + 0.2·(-2.32) + 0.1·(-3.32)]
4.​ H(X) = 0.528 + 0.522 + 0.464 + 0.332 = 1.846 bits

64. Explain the Shannon-Hartley Capacity Theorem in

detail with real-world applications.
1.​ C = B·log₂(1+S/N) defines maximum data rate for reliable communication
2.​ Application: WiFi systems adapt modulation based on SNR to approach capacity
3.​ Application: DSL technologies allocate bits to subchannels based on individual SNRs
4.​ Application: 5G systems use adaptive coding and modulation to optimize throughput

65. Discuss the limitations of Shannon's theorem in

practical communication systems.
1.​ Assumes infinite coding complexity and delay, impractical in real systems
2.​ Real channels have non-Gaussian noise and time-varying characteristics
3.​ Practical systems operate with margin below capacity due to implementation
constraints
4.​ Doesn't account for implementation complexities like synchronization and
equalization

66. How does entropy influence the efficiency of data

compression? Explain with examples.
 1.​ Entropy sets theoretical minimum bits required for lossless representation
2.​ Example: Text compression—English text has entropy ~1.3 bits/character vs. 8 bits in
ASCII
3.​ Example: JPEG—exploits lower entropy in DCT coefficients after transformation
4.​ Lower entropy sources (more predictable) allow greater compression ratios

67. Explain forward error correction techniques and

analyze their impact on communication systems.
Techniques:

1.​ Block codes (Hamming, BCH, Reed-Solomon) use algebraic structures for error
correction
2.​ Convolutional codes use state machines with memory to encode sequential data

Impact: 3. Enables reliable communication at lower SNR, extending range or reducing power
4. Trades bandwidth efficiency for improved BER performance in adverse conditions

68. Discuss in detail the role of redundancy in coding

and its effect on transmission efficiency.
1.​ Redundancy r = 1-η = (L-H)/L represents fraction of "unnecessary" bits
2.​ Controlled redundancy enables error detection and correction
3.​ Source coding aims to minimize redundancy (compression)
4.​ Channel coding adds strategic redundancy to combat channel errors

69. Explain the concept of Hamming Distance and

Hamming Weight with mathematical derivations.
Hamming Distance:

1.​ Between codewords x and y: d(x,y) = ∑|xᵢ-yᵢ| for binary symbols

2.​ Alternatively: d(x,y) = wt(x⊕y) where ⊕ is XOR and wt is Hamming weight

Hamming Weight: 3. Weight of codeword x: wt(x) = ∑xᵢ (number of 1's in x) 4. For linear
codes, minimum distance equals minimum weight of non-zero codewords

I'll provide answers to all the questions in serial order. Each answer will be concise with 4
key points as requested.

Q70: Define a continuous-time signal with an example:

1.​ A continuous-time signal is defined for every instant of time (t ∈ ℝ).

2.​ Values can take any real number within its amplitude range.
3.​ Mathematically represented as x(t), where t is a continuous variable.
 4.​ Example: A sine wave x(t) = sin(2πft) is continuous in both time and amplitude.

Q71: Define a discrete-time signal with an example:

1.​ A discrete-time signal is defined only at specific time instants, typically equally
spaced.
2.​ Represented mathematically as x[n], where n is an integer.
3.​ Exists only at discrete points in time, not between these points.
4.​ Example: A sampled sequence x[n] = {1, 2, 3, 4, 5} or a discrete sinusoid x[n] =
sin(2πFn).

Q72: What is the difference between continuous-time and discrete-time signals?

1.​ Domain: Continuous signals exist at every time instant; discrete signals exist only at
specific instants.
2.​ Representation: Continuous signals use parentheses x(t); discrete signals use
brackets x[n].
3.​ Processing: Continuous signals are processed using differential equations; discrete
signals use difference equations.
4.​ Values: Continuous signals have uncountably infinite values; discrete signals have
countable values.

Q73: What is a periodic signal? Give an example:

1.​ A periodic signal repeats itself exactly after a fixed time interval called the period.
2.​ Mathematically, x(t) = x(t + T) for continuous or x[n] = x[n + N] for discrete signals.
3.​ The fundamental period is the smallest positive value of T or N for which the equality
holds.
4.​ Example: Sine wave x(t) = sin(2πft) with period T = 1/f seconds.

Q74: What is an aperiodic signal? Give an example:

1.​ An aperiodic signal never repeats itself exactly for any time shift.
2.​ Does not satisfy x(t) = x(t + T) for any finite T > 0.
3.​ Typically has finite energy but zero average power.
4.​ Example: A rectangular pulse x(t) = rect(t/τ) or an exponential decay x(t) = e^(-at)u(t).

Q75: Define even and odd signals with suitable examples:

1.​ Even signal: x(t) = x(-t); symmetric about vertical axis; example: cos(t).
2.​ Odd signal: x(t) = -x(-t); antisymmetric about origin; example: sin(t).
3.​ Any signal can be decomposed: x(t) = xₑ(t) + xₒ(t) where xₑ(t) = [x(t) + x(-t)]/2 and
xₒ(t) = [x(t) - x(-t)]/2.
4.​ Even signals have symmetric Fourier transforms; odd signals have antisymmetric
Fourier transforms.

Q76: What is a deterministic signal? Provide an example:

1.​ A deterministic signal can be described by a mathematical function.

2.​ Future values can be predicted exactly if initial conditions are known.
 3.​ No random or probabilistic elements in its behavior.
4.​ Example: Sinusoidal signal x(t) = A·sin(ωt + φ) with known amplitude, frequency, and
phase.

Q77: Derive the mathematical representation of a continuous-time sinusoidal signal:

1.​ General form: x(t) = A·cos(ωt + φ) where A is amplitude, ω is angular frequency

(rad/s), φ is phase (rad).
2.​ Angular frequency ω = 2πf, where f is frequency in Hz; period T = 1/f = 2π/ω.
3.​ Using Euler's identity: cos(ωt + φ) = (e^j(ωt+φ) + e^-j(ωt+φ))/2.
4.​ Alternative sine representation: x(t) = A·sin(ωt + φ) = A·cos(ωt + φ - π/2).

Q78: Derive the mathematical representation of a discrete-time sinusoidal signal:

1.​ General form: x[n] = A·cos(Ωn + φ) where A is amplitude, Ω is normalized angular

frequency (rad/sample), φ is phase.
2.​ Relationship to continuous-time: Ω = ωTs where Ts is sampling period.
3.​ Period N exists if and only if Ω = 2πk/N where k, N are coprime integers.
4.​ If Ω/2π is irrational, the signal is not periodic.

Q79: Explain the differences between continuous-time and discrete-time signals with
examples:

1.​ Time domain: Continuous signals defined for all t ∈ ℝ; discrete signals defined only
at integer indices n.
2.​ Sampling: Discrete signals often result from sampling continuous signals at regular
intervals.
3.​ Processing: Continuous signals processed with analog circuits; discrete signals with
digital processors.
4.​ Examples: Continuous signal - audio waves in air; discrete signal - digital audio
samples in computer.

Q80: Explain and classify signals based on periodicity with suitable examples:

1.​ Periodic signals: Repeat after fixed intervals (e.g., sine waves, square waves); x(t) =
x(t + T).
2.​ Aperiodic signals: Never repeat exactly (e.g., single pulse, exponential decay).
3.​ Almost-periodic signals: Sum of periodic components with incommensurate periods.
4.​ Examples: Periodic - AC voltage (50/60Hz); aperiodic - lightning discharge.

Q81: Define and explain the properties of even and odd signals with mathematical
proofs:

1.​ Even signal property: x(-t) = x(t); odd signal property: x(-t) = -x(t).
2.​ Product of two even or two odd signals is even; product of even and odd signal is
odd.
3.​ Convolution of even signals is even; convolution of odd signals is odd.
4.​ Mathematical proof for decomposition: x(t) = [x(t) + x(-t)]/2 + [x(t) - x(-t)]/2 = xₑ(t) +
xₒ(t).
Q82: What are deterministic and random signals? Explain with examples:

1.​ Deterministic signals: Exactly predictable (e.g., sine wave, step function); described
by explicit mathematical equations.
2.​ Random signals: Unpredictable and described statistically (e.g., noise, speech);
characterized by probability distributions.
3.​ Semi-deterministic signals: Combination of deterministic and random components
(e.g., modulated signals with noise).
4.​ Examples: Deterministic - clock pulse; random - thermal noise in electronic circuits.

Q83: Explain the classification of continuous-time and discrete-time signals with

suitable examples:

1.​ Energy signals: Finite energy, zero power (e.g., pulse signal); ∫|x(t)|²dt < ∞.
2.​ Power signals: Finite power, infinite energy (e.g., sine wave); lim(T→∞) 1/2T ∫|x(t)|²dt
< ∞.
3.​ Causal signals: Zero for negative time (e.g., step function); x(t) = 0 for t < 0.
4.​ Bounded signals: Magnitude never exceeds finite value (e.g., sinusoid); |x(t)| ≤ M <
∞.

Q84: Derive the mathematical representation of a continuous-time sinusoidal signal

and explain its properties:

1.​ Expression: x(t) = A·cos(ωt + φ); A = amplitude, ω = angular frequency, φ = phase.

2.​ Properties: Periodic with T = 2π/ω; power signal with average power P = A²/2.
3.​ Orthogonality: Sinusoids with different frequencies are orthogonal over one period.
4.​ Frequency domain: Transforms to impulse pairs at ±ω in the frequency domain.

Q85: Derive the mathematical representation of a discrete-time sinusoidal signal and

explain its properties:

1.​ Expression: x[n] = A·cos(Ωn + φ); A = amplitude, Ω = normalized angular frequency,

φ = phase.
2.​ Periodicity: Period N if Ω = 2πk/N with k, N coprime integers.
3.​ Aliasing effect: Frequencies Ω and Ω + 2πk are indistinguishable in discrete domain.
4.​ Orthogonality: Discrete sinusoids with different frequencies are orthogonal over one
period.

Q86: Explain and derive the conditions for a signal to be periodic in both continuous
and discrete-time domains:

1.​ Continuous-time condition: x(t) = x(t + T) where T > 0 is the period.

2.​ Discrete-time condition: x[n] = x[n + N] where N is a positive integer.
3.​ For sum of sinusoids: x(t) = Σᵢ Aᵢcos(ωᵢt + φᵢ), periodic if ratios ωᵢ/ω₁ are rational.
4.​ For discrete sinusoid x[n] = cos(Ωn): Period N exists only if Ω = 2πk/N with k, N
coprime.

Q87: Compare and contrast continuous-time and discrete-time signals in terms of

representation, analysis, and applications:
 1.​ Representation: CT uses differential equations, DT uses difference equations.
2.​ Analysis: CT uses Fourier/Laplace transforms, DT uses Z-transform/DTFT.
3.​ Processing: CT requires analog hardware, DT uses digital processors.
4.​ Applications: CT in natural phenomena, analog electronics; DT in digital
communications, DSP.

Q88: Define and derive the conditions for even and odd signals with mathematical
proofs and graphical representations:

1.​ Even signal condition: x(-t) = x(t); graphically symmetric about vertical axis.
2.​ Odd signal condition: x(-t) = -x(t); graphically symmetric about origin.
3.​ Decomposition proof: x(t) = [x(t) + x(-t)]/2 + [x(t) - x(-t)]/2.
4.​ Properties: Integral of odd function over symmetric limits = 0; integral of even function
is symmetric.

Q89: Explain deterministic and random signals with proper examples and their
significance in communication systems:

1.​ Deterministic signals (carrier waves, digital pulses) provide reliability and
predictability in communications.
2.​ Random signals (noise, information signals) require statistical characterization; affect
system reliability.
3.​ Communication systems combine both: deterministic carriers modulated by random
information.
4.​ Signal-to-noise ratio (SNR) quantifies the ratio of deterministic signal power to
random noise power.

Q90: Define and derive the conditions for energy and power signals with
mathematical expressions and examples:

1.​ Energy signal: Finite total energy (∫|x(t)|²dt < ∞); zero average power; example: pulse
signal.
2.​ Power signal: Finite average power (lim(T→∞) 1/2T ∫|x(t)|²dt < ∞); infinite energy;
example: sinusoid.
3.​ Signals can be neither energy nor power signals (e.g., x(t) = t).
4.​ Periodic signals are always power signals with average power = 1/T ∫|x(t)|²dt over
one period.

Q91: Find whether the signal is causal or not. y(n) = u(n + 3) - u(n - 2):

1.​ A causal signal is zero for negative time (n < 0).

2.​ For y(n) = u(n + 3) - u(n - 2), expand terms: u(n + 3) = 1 for n ≥ -3; u(n - 2) = 1 for n ≥
2.
3.​ For n < 0, y(n) = 1 - 0 = 1 (when -3 ≤ n < 0).
4.​ Since y(n) ≠ 0 for some n < 0, the signal is non-causal.

Q92: Determine whether the given system described by the equation is linear or not.
y(n) = n·x(n):
 1.​ System is linear if it satisfies superposition principle: T[αx₁(n) + βx₂(n)] = αT[x₁(n)] +
βT[x₂(n)].
2.​ For input αx₁(n) + βx₂(n): y(n) = n·[αx₁(n) + βx₂(n)] = αn·x₁(n) + βn·x₂(n).
3.​ For individual inputs: T[x₁(n)] = n·x₁(n) and T[x₂(n)] = n·x₂(n).
4.​ Since αT[x₁(n)] + βT[x₂(n)] = αn·x₁(n) + βn·x₂(n), the system is linear.

Q93: Find the linear convolution of x(n)={1, 2, 3} with h(n)={2, 4}:

1.​ Convolution formula: y(n) = x(n) * h(n) = Σ x(k)·h(n-k).

2.​ Calculate y(0) = x(0)·h(0) = 1·2 = 2.
3.​ Calculate y(1) = x(0)·h(1) + x(1)·h(0) = 1·4 + 2·2 = 8.
4.​ Calculate y(2) = x(1)·h(1) + x(2)·h(0) = 2·4 + 3·2 = 14, y(3) = x(2)·h(1) = 3·4 = 12;
result: y(n) = {2, 8, 14, 12}.

Q94: Is the discrete time system described by the difference equation y(n) = x(-n) is
causal?

1.​ A causal system's output at time n depends only on present and past inputs.
2.​ For y(n) = x(-n), the output at n depends on input at time -n.
3.​ When n > 0, output depends on input at negative time (-n < 0), which is in the past.
4.​ When n < 0, output depends on input at positive time (-n > 0), which is in the future;
therefore, system is non-causal.

Q95: Find out the range of values of the parameter 'a' for which the linear time
invariant system with impulse response h(n) = aⁿu(n) is stable:

1.​ BIBO stability requires Σ|h(n)| < ∞.

2.​ For h(n) = aⁿu(n), the sum is Σₙ₌₀^∞ |a|ⁿ.
3.​ This geometric series converges only when |a| < 1.
4.​ Therefore, the system is stable for -1 < a < 1.

Q96: Define continuous-time (CT) and discrete-time (DT) systems with examples:

1.​ CT systems: Process continuous-time inputs to produce continuous-time outputs;

described by differential equations.
2.​ DT systems: Process discrete-time inputs to produce discrete-time outputs;
described by difference equations.
3.​ CT example: RC circuit with input-output relation RC(dy(t)/dt) + y(t) = x(t).
4.​ DT example: Digital filter with input-output relation y[n] = 0.5y[n-1] + x[n].

Q97: What is a linear time-invariant (LTI) system?

1.​ Linear: Satisfies superposition principle; response to sum equals sum of individual
responses.
2.​ Time-invariant: Time-shifted input produces identical time-shifted output.
3.​ Completely characterized by impulse response through convolution relationship.
4.​ Key properties: Zero-input implies zero-output; memoryless if impulse response is an
impulse; stability if impulse response is absolutely summable.

Q98: Differentiate between static and dynamic systems:

 1.​ Static system: Output depends only on current input; no memory of past inputs.
2.​ Dynamic system: Output depends on current and past inputs/outputs; exhibits
memory.
3.​ Static example: Resistive circuit y(t) = R·x(t); instantaneous response.
4.​ Dynamic example: Capacitive circuit that integrates input; retains memory of past
values.

Q99: What are the basic classifications of CT and DT systems?

1.​ Linear vs. nonlinear: Based on superposition principle.

2.​ Time-invariant vs. time-variant: Based on time-shift properties.
3.​ Causal vs. non-causal: Based on dependence on future inputs.
4.​ Stable vs. unstable: Based on bounded-input bounded-output behavior.

Q100: Define causal and non-causal systems with examples:

1.​ Causal system: Output depends only on present and past inputs; physically
realizable.
2.​ Non-causal system: Output depends on future inputs; not physically realizable in
real-time.
3.​ Causal example: Physical RC filter with impulse response h(t) = e^(-t/RC)u(t).
4.​ Non-causal example: Ideal low-pass filter with sinc impulse response h(t) =
sin(ωct)/(πt).

Q101: What is the importance of system classification in signal processing?

1.​ Identifies implementable systems (causal, stable) for real-world applications.

2.​ Determines appropriate mathematical tools and analysis methods.
3.​ Helps predict system behavior under various input conditions.
4.​ Guides design choices and optimization strategies for specific requirements.

Q102: Define impulse response and its significance in system analysis:

1.​ Impulse response is the system's output when input is a unit impulse (Dirac delta or
unit sample).
2.​ Completely characterizes an LTI system's behavior for any input.
3.​ Output for any input can be calculated via convolution with impulse response.
4.​ Time-domain counterpart of the system's transfer function in frequency domain.

Q103: Find the linear convolution of x(n)={1, 2, 3, 4, 5, 6, 7} with h(n)={2, 4, 6, 8}:

1.​ Convolution formula: y(n) = Σ x(k)·h(n-k).

2.​ Length of output: (N₁+N₂-1) = 7+4-1 = 10 samples.
3.​ First few terms: y(0) = 2; y(1) = 4 + 4 = 8; y(2) = 6 + 8 + 6 = 20.
4.​ Complete result: y(n) = {2, 8, 20, 40, 66, 92, 114, 112, 84, 56}.

Q104: Find the autocorrelation of {1,2,1,3}:

 1.​ Autocorrelation: r[k] = Σₙ x[n]·x[n+k].
2.​ For k = 0: r[0] = 1² + 2² + 1² + 3² = 15 (energy of signal).
3.​ For k = 1: r[1] = 1·2 + 2·1 + 1·3 = 7; r[-1] = r[1] = 7 (autocorrelation is even).
4.​ For k = 2: r[2] = 1·1 + 2·3 = 7; r[-2] = 7; For k = 3: r[3] = 1·3 = 3; r[-3] = 3.

Q105: Given an LTI system with the impulse response h(t), compute the step response
of the system:

1.​ Step response s(t) = impulse response h(t) convolved with unit step u(t).
2.​ Mathematically: s(t) = h(t) * u(t) = ∫₀ᵗ h(τ)dτ.
3.​ Step response is the integral (accumulation) of impulse response.
4.​ In frequency domain: S(ω) = H(ω)/jω (except at ω = 0).

Q106: Calculate the convolution sum for the analysis of an LTI system, where the
input signal x[n] = {1, 2, 3, 2, 1}, and the system's impulse response is h[n] = {0.5, 1,
0.5}:

1.​ Convolution formula: y[n] = x[n] * h[n] = Σ x[k]·h[n-k].

2.​ Length of output: 5+3-1 = 7 samples.
3.​ Calculations: y[0] = 0.5; y[1] = 1+1 = 2; y[2] = 1.5+2+0.5 = 4; y[3] = 0.5·3+1·2+0.5·1 =
4.
4.​ Complete result: y[n] = {0.5, 2, 4, 4, 3, 1.5, 0.5}.

Q107: Identify the given system for linearity, causality, static/dynamic. Y(t)=t·x(t):

1.​ Linearity: Y(ax₁(t)+bx₂(t)) = t·(ax₁(t)+bx₂(t)) = a·t·x₁(t) + b·t·x₂(t) = aY₁(t) + bY₂(t);

system is linear.
2.​ Causality: Output at time t depends only on input at same time t; system is causal.
3.​ Memory: Output depends only on current input value, not past values; system is
static.
4.​ Time-invariance: If x(t) → y(t), then x(t-τ) → (t-τ)·x(t-τ) ≠ y(t-τ) = t·x(t-τ); system is
time-variant.

Q108: Identify the given system for time variance, stability, static/dynamic. Y(t)=x(-t):

1.​ Time-variance: If x(t) → y(t) = x(-t), then x(t-τ) → x(-t+τ) ≠ y(t-τ) = x(-t+τ); system is
time-variant.
2.​ Stability: For bounded input |x(t)| ≤ M, output |y(t)| = |x(-t)| ≤ M is also bounded;
system is stable.
3.​ Causality: Output at time t depends on input at time -t (future for t < 0); system is
non-causal.
4.​ Memory: Output depends only on input at different time instant; system is static.

Q109: Explain the differences between continuous-time (CT) and discrete-time (DT)
systems with suitable examples:

1.​ CT systems operate on continuous-time signals; DT systems operate on

discrete-time sequences.
2.​ CT systems described by differential equations; DT systems by difference equations.
 3.​ CT example: RC circuit with y'(t) + y(t)/RC = x(t)/RC; DT example: digital filter y[n] =
0.9y[n-1] + x[n].
4.​ CT systems analyzed using Laplace/Fourier transforms; DT systems using
Z-transform/DTFT.

Q110: Define and classify different types of CT and DT systems with examples:

1.​ Linear/nonlinear: Linear obeys superposition (RC circuit); nonlinear doesn't (amplifier
with saturation).
2.​ Time-invariant/time-variant: Invariant parameters don't change (RLC circuit); variant
parameters change (varying resistor).
3.​ Causal/non-causal: Causal depends only on past/present (practical filters);
non-causal uses future (ideal filters).
4.​ Stable/unstable: Stable produces bounded outputs for bounded inputs (passive
circuits); unstable doesn't (oscillators).

Q111: Explain linear and nonlinear systems with examples:

1.​ Linear systems: Satisfy superposition principle; output for sum equals sum of
individual outputs.
2.​ Nonlinear systems: Violate superposition; response to sum differs from sum of
responses.
3.​ Linear example: Audio amplifier in normal range; y(t) = K·x(t).
4.​ Nonlinear example: Clipping circuit with saturation; y(t) = sat(x(t)).

Q112: Describe the significance of static and dynamic systems in signal processing:

1.​ Static systems: Memoryless, instantaneous response; suitable for amplitude scaling,
nonlinear transformations.
2.​ Dynamic systems: Memory-dependent, temporal response; enable filtering,
integration, differentiation.
3.​ Static systems have simpler implementation but limited functionality in signal
processing.
4.​ Dynamic systems enable frequency-selective filtering, essential for most signal
processing applications.

Q113: Discuss the concept of memoryless systems and their applications:

1.​ Memoryless systems: Output depends only on current input; y(t) = f(x(t)).
2.​ No energy storage elements; instantaneous input-output relationship.
3.​ Applications: Level shifting, amplitude scaling, nonlinear distortion, thresholding.
4.​ Examples: Resistive circuits, instantaneous companders, hard limiters, quantizers.

Q114: Explain the difference between time-invariant and time-variant systems with
examples:

1.​ Time-invariant: Time shift in input causes identical time shift in output; properties
don't change with time.
2.​ Time-variant: System parameters or characteristics change with time.
 3.​ Time-invariant example: Fixed RC filter; time-variant example: Variable gain amplifier.
4.​ Mathematical test: If x(t) → y(t), then x(t-τ) → y(t-τ) for time-invariant systems.

Q115: Explain in detail the differences between continuous-time (CT) and

discrete-time (DT) systems with suitable examples and applications:

1.​ CT systems process analog signals continuously in time; DT systems process

samples at discrete time instants.
2.​ CT implementations use analog components (resistors, capacitors); DT systems use
digital hardware or software.
3.​ CT applications: Analog filters, audio amplifiers, analog control systems; DT
applications: Digital filters, image processing, digital communications.
4.​ CT systems limited by component tolerances; DT systems by sampling rate and
quantization effects.

Q116: Derive the mathematical representation of a general CT and DT system:

1.​ CT system: y(t) = T[x(t)] where T is the transformation operator; for LTI: y(t) =
∫h(t-τ)x(τ)dτ.
2.​ DT system: y[n] = T[x[n]]; for LTI: y[n] = Σ h[n-k]x[k].
3.​ CT differential equation form: Σₘ ₌₀a (dᵏy(t)/dtᵏ) = Σⁿⱼ₌₀bⱼ(dʲx(t)/dtʲ).
4.​ DT difference equation form: Σₘ ₌₀a y[n-k] = Σⁿⱼ₌₀bⱼx[n-j].

Q117: Determine the linear convolution of x(n) = {1,1,1,1} and h(n)= {2,2} using
graphical representation:

1.​ Flip h[n] to h[-n] = {2,2} and shift along x[n].

2.​ For each position, multiply overlapping terms and sum.
3.​ For n = 0, 1, 2, 3, 4, 5: y[0] = 2, y[1] = 4, y[2] = 4, y[3] = 4, y[4] = 2, y[5] = 0.
4.​ Result: y[n] = {2, 4, 4, 4, 2}.

Q118: Determine the linear convolution of x(t)=u(t) and h(t)=u(t+2)-u(t-5) using

graphical representation:

1.​ Flip h(t) to h(-t) = u(-t+2)-u(-t-5) = u(t-2)-u(t+5).

2.​ Convolve: y(t) = ∫x(τ)h(t-τ)dτ.
3.​ For t < 2: y(t) = 0; for 2 ≤ t < 7: y(t) = t-2; for t ≥ 7: y(t) = 7.
4.​ Result: y(t) = (t-2)·[u(t-2)-u(t-7)] + 7·u(t-7).

Q119: Identify the given system for linearity, causality, time variance, stability,
static/dynamic. Y(t)=x(t)+3x(t+4):

1.​ Linearity: Y(ax₁(t)+bx₂(t)) = a·Y(x₁(t)) + b·Y(x₂(t)); system is linear.

2.​ Causality: Output at time t depends on input at t+4 (future); system is non-causal.
3.​ Time-invariance: For shifted input x(t-τ), output is x(t-τ)+3x(t-τ+4) = y(t-τ); system is
time-invariant.
4.​ Stability: For bounded input, output remains bounded; system is stable; dynamic as it
uses input at different times.
Q120: Identify the given system for linearity, causality, time variance, stability,
static/dynamic. Y(t)=t² x(t):

1.​ Linearity: Y(ax₁(t)+bx₂(t)) = t²·(ax₁(t)+bx₂(t)) = a·t²x₁(t) + b·t²x₂(t) = aY₁(t) + bY₂(t);

system is linear.
2.​ Causality: Output at time t depends only on input at same time t; system is causal.
3.​ Time-invariance: For shifted input x(t-τ), output is (t)²·x(t-τ) ≠ (t-τ)²·x(t-τ); system is
time-variant.
4.​ Stability: For large t, output may exceed bounds even for bounded input; potentially
unstable; static system.

Q121: Identify the given system for linearity, causality, time variance, stability,
static/dynamic. Y(t)=x(t)+tx(t):

1.​ Linearity: Y(ax₁(t)+bx₂(t)) = (1+t)·(ax₁(t)+bx₂(t)) = a(1+t)x₁(t) + b(1+t)x₂(t) = aY₁(t) +

bY₂(t); system is linear.
2.​ Causality: Output depends only on current input; system is causal.
3.​ Time-invariance: For shifted input x(t-τ), output is (1+t)·x(t-τ) ≠ (1+(t-τ))·x(t-τ); system
is time-variant.
4.​ Stability: For bounded input |x(t)| ≤ M, output |(1+t)x(t)| may grow unbounded as t
increases; potentially unstable; static system.

Q122: Find the linear convolution of x(n)={1, -2, 3, 4, 5, -6, 7} with h(n)={2, 4, 6, -8, 10}
where the BOLD letter is value at origin:

1.​ Assuming origin at x[0]=1 and h[0]=2.

2.​ Result length: 7+5-1 = 11 samples.
3.​ First few values: y[0] = 2; y[1] = 4 - 4 = 0; y[2] = 6 - 8 + 6 = 4.
4.​ Complete result: y[n] = {2, 0, 4, 22, -3, 2, 71, -18, -92, -60, 70}.

Q123: Classify different types of CT and DT systems and justify their classification
with real-world examples:

1.​ Linear/nonlinear: Linear - small-signal amplifiers (superposition applies); nonlinear -

audio compressors (superposition fails).
2.​ Time-invariant/time-variant: Invariant - fixed filters; variant - adaptive filters that adjust
parameters.
3.​ Causal/non-causal: Causal - real-time audio processing; non-causal - offline image
enhancement.
4.​ BIBO stable/unstable: Stable - passive filters; unstable - positive feedback amplifiers,
oscillators.

Q124: Explain the significance of causality and stability in system analysis and their
impact on real-world applications:

1.​ Causality ensures physical realizability for real-time systems; essential for live signal
processing.
2.​ Stability prevents unbounded outputs; crucial for system reliability and preventing
damage.
 3.​ Non-causal systems can be implemented with delay in offline processing for
improved performance.
4.​ Unstable systems have controlled applications in oscillators, triggers, and
regenerative circuits.

Q125: Compare and contrast time-invariant and time-variant systems with practical
examples:

1.​ Time-invariant: Fixed parameters regardless of when input is applied; example:

traditional filters.
2.​ Time-variant: Parameters change with time; example: automatic gain control,
adaptive filters.
3.​ Time-invariant systems easier to analyze with Fourier/Laplace/Z transforms;
time-variant systems require time-dependent analysis.
4.​ Practical examples: Time-invariant - passive RLC filters; time-variant - Doppler radar,
frequency modulation systems.

Q126: What is a BIBO stable system? Derive and explain the mathematical condition
for stability:

1.​ BIBO (Bounded-Input Bounded-Output) stable system: Bounded input always

produces bounded output.
2.​ For continuous LTI: Stability condition is ∫|h(t)|dt < ∞ (impulse response absolutely
integrable).
3.​ For discrete LTI: Stability condition is Σ|h[n]| < ∞ (impulse response absolutely
summable).
4.​ In frequency domain: All poles of transfer function must lie in left half-plane (CT) or
inside unit circle (DT).

Q127: Discuss the practical implications of static and dynamic systems in

engineering applications:

1.​ Static systems: Simpler implementation, lower cost, but limited functionality (e.g.,
level shifters, amplifiers).
2.​ Dynamic systems: More complex, higher cost, but enable filtering, integration, control
(e.g., filters, PID controllers).
3.​ Static systems suitable for instantaneous transformations; dynamic systems needed
for temporal processing.
4.​ Engineering trade-off: Static systems for simple tasks, dynamic systems when
memory/history processing required.

Q128: Define and explain invertible systems. How does invertibility affect system
performance?

1.​ Invertible system: Output can be processed by another system to recover exact
input.
2.​ Mathematical condition: One-to-one mapping between inputs and outputs.
3.​ Invertibility enables perfect signal recovery, error correction, and system cascading.
 4.​ Non-invertible systems (like quantizers) cause irreversible information loss, limiting
performance.

Q129: Define Global System for Mobile Communications (GSM):

1.​ GSM is a digital cellular network standard for mobile communications.

2.​ Utilizes TDMA/FDMA multiple access techniques with frequency bands around
900/1800/1900 MHz.
3.​ Provides voice calls, SMS, and data services with end-to-end encryption.
4.​ First deployed in 1991, became world's most widespread mobile standard before
4G/5G.

Q130: What is Code Division Multiple Access (CDMA)?

1.​ CDMA is a channel access method utilizing spread spectrum technology.

2.​ Multiple users transmit simultaneously on same frequency using unique spreading
codes.
3.​ Signals separated by correlation receivers using code orthogonality properties.
4.​ Offers increased capacity, improved security, and resistance to interference
compared to TDMA/FDMA.

Q131: Explain the Cellular Concept in mobile communication:

1.​ Geographic area divided into hexagonal cells, each served by base station with
limited frequency set.
2.​ Frequencies reused in non-adjacent cells to increase capacity.
3.​ Handover mechanism allows continuous service as users move between cells.
4.​ System capacity increases by cell splitting and reducing transmitter power.

Q132: What is Frequency Reuse in cellular networks?

1.​ Process of using same frequencies in multiple non-adjacent cells to increase

capacity.
2.​ Characterized by reuse factor N (typically 3, 4, 7); determines distance between
co-channel cells.
3.​ Trade-off between system capacity and interference levels.
4.​ Enables efficient spectrum utilization within limited bandwidth allocation.

Q133: List the different Multiple Access Schemes used in communication:

1.​ FDMA (Frequency Division Multiple Access): Assigns unique frequency bands to
users.
2.​ TDMA (Time Division Multiple Access): Assigns unique time slots to users on same
frequency.
3.​ CDMA (Code Division Multiple Access): Users share frequency/time using unique
orthogonal codes.
4.​ OFDMA (Orthogonal Frequency Division Multiple Access): Combines TDMA and
FDMA principles with orthogonal subcarriers.

Q134: Define Satellite Communication and its applications:

 1.​ Communication system using satellites as signal relay points between earth stations.
2.​ Types: GEO (36,000 km), MEO (2,000-36,000 km), LEO (below 2,000 km) satellites.
3.​ Applications: Television broadcasting, telephone services, internet connectivity,
navigation.
4.​ Advantages: Wide coverage area, independent of terrestrial infrastructure,
disaster-resilient.

Q135: What is Time Division Multiple Access (TDMA)?

1.​ Channel access method dividing signal into time slots assigned to different users.
2.​ Users transmit in rapid succession on same frequency but in different time slots.
3.​ Requires precise timing synchronization between transmitters and receivers.
4.​ Used in GSM, DECT cordless phones, and satellite systems.

Q136: Explain the architecture of Global System for Mobile Communications (GSM)
with a neat diagram:

1.​ Mobile Station (MS): Handset and SIM card for user authentication.
2.​ Base Station Subsystem (BSS): BTS (Base Transceiver Station) and BSC (Base
Station Controller).
3.​ Network Switching Subsystem: MSC (Mobile Switching Center), HLR/VLR
(Home/Visitor Location Registers), AuC (Authentication Center).
4.​ Operation and Support Subsystem: Manages network operation, maintenance, and
subscriber services.

Continuing with the remaining questions:

Q137: Describe the working principle of Code Division Multiple Access (CDMA):

1.​ Each user assigned unique pseudorandom spreading code with chip rate much
higher than data rate.
2.​ User data multiplied by spreading code (spreading); transmitted simultaneously with
other users' signals.
3.​ Receiver correlates received signal with specific user's code to extract only that
user's data (despreading).
4.​ Multiple users separated through code orthogonality; provides resistance to
narrowband interference and jamming.

Q138: Explain the concept of Cellular Frequency Reuse with an example:

1.​ Available frequency spectrum divided into channel sets (e.g., A, B, C for reuse factor
of 3).
2.​ Each cell assigned one channel set; same set reused in cells separated by sufficient
distance.
3.​ Example: In 7-cell reuse pattern, cells labeled A-G, with minimum distance D =
R√(3N) between co-channel cells.
4.​ Reduces interference while maximizing spectrum utilization; trade-off between
capacity and quality.
Q139: What are the different Multiple Access Schemes used in mobile
communication?

1.​ FDMA: Divides spectrum into frequency bands (e.g., early analog systems like
AMPS).
2.​ TDMA: Divides channel into time slots (e.g., GSM uses 8 slots per carrier).
3.​ CDMA: Users share frequency/time using unique codes (e.g., IS-95, WCDMA).
4.​ SDMA: Uses directional antennas to separate users spatially (e.g., smart antennas,
MIMO systems).

Q140: Discuss the advantages and disadvantages of Satellite Communication:

1.​ Advantages: Wide coverage area, rapid deployment, broadcast capability,

independent of terrestrial infrastructure.
2.​ Disadvantages: High propagation delay (especially for GEO), signal attenuation,
expensive equipment, vulnerable to weather.
3.​ Transmission limitations: Limited bandwidth, power constraints, orbital slot
congestion.
4.​ Economic factors: High initial investment, ongoing operational costs, limited lifespan
(10-15 years).

Q141: Explain the role of base stations in cellular networks:

1.​ Provide radio coverage within cell area; interface between mobile devices and core
network.
2.​ Handle radio resource management: channel allocation, power control, handover
initiation.
3.​ Perform signal processing: modulation/demodulation, encoding/decoding, error
correction.
4.​ Monitor and maintain connection quality; manage interference with adjacent cells.

Q142: Explain the Global System for Mobile Communications (GSM) architecture with
a neat diagram:

1.​ Mobile Station: User equipment with SIM card for authentication and subscriber
identity.
2.​ Base Station Subsystem: BTS (radio transmission/reception), BSC (radio resource
management).
3.​ Network Switching Subsystem: MSC (switching), HLR/VLR (location databases),
AuC/EIR (security).
4.​ Operation Support Subsystem: Network management, monitoring, billing, subscriber
administration.

Q143: Describe in detail the working principle of Code Division Multiple Access
(CDMA):

1.​ Spread spectrum technique: Data signal spread across wide bandwidth using unique
spreading code.
 2.​ Spreading process: User data (bits) multiplied by high-rate spreading code (chips);
increases bandwidth.
3.​ Multiple access capability: Users distinguished by code orthogonality; receiver
correlates with specific code.
4.​ System benefits: Frequency reuse factor of 1, soft handoff capability, resistance to
multipath fading, inherent security.

Q144: Explain the Cellular Concept and Frequency Reuse with an example:

1.​ Cellular concept: Service area divided into cells with base stations; enables mobility
and frequency reuse.
2.​ Frequency reuse: Same frequencies reused in non-adjacent cells based on reuse
pattern (N).
3.​ Example: With 120 channels and reuse factor N=4, each cell gets 30 channels;
capacity increases by cell splitting.
4.​ Co-channel interference controlled by distance D = R√(3N) between cells using same
frequencies.

Q145: Compare and contrast FDMA, TDMA, and CDMA techniques with advantages
and disadvantages:

1.​ FDMA: Users assigned fixed frequency bands; simple implementation; inefficient for
bursty traffic; guard bands reduce spectrum efficiency.
2.​ TDMA: Users share frequency with different time slots; efficient for voice; requires
synchronization; vulnerable to multipath fading.
3.​ CDMA: Users share frequency/time with unique codes; high capacity; soft handoff
capability; complex power control required.
4.​ Evolution trend: From FDMA (1G) to TDMA (2G) to CDMA/OFDMA (3G/4G/5G) for
increased capacity and performance.

Q146: Describe the Multiple Access Schemes used in mobile communication:

1.​ FDMA: Channel bandwidth divided into sub-bands; used in 1G systems; each user
allocated fixed frequency.
2.​ TDMA: Time domain divided into slots; used in 2G (GSM); multiple users share same
frequency band.
3.​ CDMA: Users differentiated by codes; used in 3G; all users transmit simultaneously
across entire bandwidth.
4.​ OFDMA: Combines FDMA and TDMA on orthogonal subcarriers; used in 4G/5G;
efficient for high-speed data.

Q147: What are the main components of a satellite communication system, and how
do they work?

1.​ Space segment: Satellites with transponders that receive, amplify, and retransmit
signals.
2.​ Ground segment: Earth stations that transmit/receive signals, perform baseband
processing, and network control.
 3.​ User segment: Terminals that connect to satellites (VSAT, satellite phones, broadcast
receivers).
4.​ Control segment: Tracking, telemetry, command facilities that monitor and maintain
satellite positioning.

Q148: Explain the different modulation techniques used in GSM and CDMA:

1.​ GSM uses GMSK (Gaussian Minimum Shift Keying): Binary data modulated through
frequency shifts; controlled bandwidth through Gaussian filtering.
2.​ CDMA uses QPSK/OQPSK (Quadrature/Offset Phase Shift Keying): Data modulated
onto I/Q carriers; better spectral efficiency.
3.​ GSM modulation rate: 270.833 kbps with spectrum efficiency of 1.35 bits/Hz.
4.​ CDMA uses variable rate modulation with spreading factors; adapts to service
requirements.

Q149: What is the role of spread spectrum techniques in CDMA?

1.​ Provides multiple access capability through code division rather than frequency/time
division.
2.​ Enhances security through signal spreading; appears as noise to unauthorized
receivers.
3.​ Improves resistance to narrowband interference and jamming through processing
gain.
4.​ Enables multipath diversity utilization through rake receivers; improves performance
in fading channels.

Q150: Explain the impact of bandwidth limitations on digital communication:

1.​ Restricts maximum achievable data rate according to Shannon-Hartley theorem: C =

B·log₂(1+SNR).
2.​ Causes intersymbol interference (ISI) when symbol rate exceeds available
bandwidth.
3.​ Forces trade-offs between data rate, power efficiency, and error performance.
4.​ Necessitates advanced techniques: higher-order modulation, channel coding, and
spectrum-efficient algorithms.

Q151: Compare the performance of phase modulation and frequency modulation in

noise environments:

1.​ FM provides better noise immunity at high modulation indices due to capture effect.
2.​ PM generally more susceptible to phase noise but offers better spectral efficiency.
3.​ FM exhibits threshold effect: performance degrades rapidly below critical SNR
threshold.
4.​ PM provides more consistent performance across SNR range; preferred for digital
signals.

Q152: Discuss the significance of pulse modulation in industrial automation:

1.​ Provides noise immunity in electrically noisy industrial environments.

 2.​ Enables long-distance transmission with minimal signal degradation.
3.​ Facilitates multiplexing of multiple sensor signals on single communication line.
4.​ Supports digital interfacing with controllers, computers, and networked systems.

Q153: Explain the significance of modulation in communication systems:

1.​ Enables efficient transmission by shifting signals to appropriate frequency bands.

2.​ Facilitates multiplexing of multiple signals in shared medium.
3.​ Improves signal characteristics for transmission (noise immunity, bandwidth
utilization).
4.​ Allows adaptation to channel conditions and service requirements.

Q154: Explain the need for synchronization in digital communication:

1.​ Ensures proper sampling of received signal at optimal decision points.

2.​ Facilitates correct demodulation by maintaining phase/frequency alignment.
3.​ Enables accurate symbol/frame/packet identification and boundaries.
4.​ Minimizes bit error rate by preventing timing drift between transmitter and receiver.

Q155: Explain the trade-off between bandwidth and power efficiency in modulation
techniques:

1.​ Higher-order modulation (e.g., 64-QAM) increases bits/symbol and bandwidth

efficiency but requires higher SNR.
2.​ Binary modulation schemes (BPSK, BFSK) offer better power efficiency but lower
spectral efficiency.
3.​ Shannon limit defines theoretical boundary of this trade-off; C/B = log₂(1+SNR).
4.​ Practical systems balance these factors based on application requirements and
channel conditions.

Q156: Compare the effectiveness of Phase Modulation (PM) and Frequency

Modulation (FM) under noise conditions:

1.​ FM provides superior performance in high SNR conditions due to wideband noise
suppression.
2.​ PM maintains more consistent performance across SNR range; less affected by
threshold effect.
3.​ FM's noise immunity improves with modulation index; PM's performance more
directly tied to SNR.
4.​ Both outperform amplitude modulation in noise; FM preferred for audio/analog, PM
for digital.

Q157: Analyze the effect of jitter in digital communication systems:

1.​ Causes timing uncertainty in sampling instants; degrades bit error rate performance.
2.​ Accumulates in long transmission chains; limits maximum achievable data rate.
3.​ Critical in high-speed systems; requires precise clock recovery circuits.
4.​ Mitigation techniques: phase-locked loops, elastic buffers, jitter attenuators.
Q158: Design a secure voice communication system using PCM and justify your
approach:

1.​ PCM sampling at 8 kHz with 8-bit quantization for telephone-quality voice.
2.​ AES encryption with 256-bit keys for secure transmission.
3.​ Forward Error Correction (Reed-Solomon codes) for reliability in noisy channels.
4.​ Authentication mechanism using digital signatures to prevent unauthorized access.

Q159: How can digital modulation techniques enhance communication in IoT

networks?

1.​ Low-power modulation schemes (FSK, BPSK) extend battery life in IoT devices.
2.​ Adaptive modulation adjusts data rate based on channel quality and power
constraints.
3.​ Spread spectrum techniques provide robustness in crowded spectrum environments.
4.​ Advanced schemes like LoRa CSS enable long-range, low-power communication for
widespread sensor networks.

Q160: Why do we still rely on analog modulation techniques despite digital

advancements?

1.​ Simplicity and low cost for basic applications (e.g., AM/FM broadcasting).
2.​ Lower latency without digital processing delays for time-critical systems.
3.​ Natural compatibility with analog sensors and legacy infrastructure.
4.​ Better spectral efficiency for certain continuous analog signals (voice, music).

Q161: How can modulation techniques evolve to support terabit wireless

communication?

1.​ Ultra-high order modulation schemes (1024+ QAM) with advanced equalization.
2.​ Massive MIMO with spatial multiplexing to increase capacity through parallel
streams.
3.​ Millimeter wave and THz band utilization with specialized modulation for high
frequencies.
4.​ AI-optimized adaptive modulation responding dynamically to channel conditions.

Q162: Why is synchronization increasingly critical for next-generation wireless

systems?

1.​ Higher frequencies (mmWave, THz) are more susceptible to phase noise and timing
errors.
2.​ Ultra-dense networks require precise synchronization for interference management.
3.​ Advanced techniques (carrier aggregation, coordinated multipoint) depend on tight
timing.
4.​ Real-time applications (autonomous vehicles, tactile internet) demand
microsecond-level accuracy.

Q163: Compare digital modulation techniques in terms of power and spectral

efficiency:
 1.​ BPSK: 1 bit/symbol, excellent power efficiency (lowest Eb/N0), poor spectral
efficiency.
2.​ QPSK: 2 bits/symbol, good power efficiency, double spectral efficiency of BPSK.
3.​ 16-QAM: 4 bits/symbol, moderate power efficiency, high spectral efficiency.
4.​ 64-QAM+: Very high spectral efficiency, poor power efficiency, requires high SNR.

Q164: How does multipath fading affect the performance of digital modulation
techniques?

1.​ Causes frequency-selective fading; different frequencies experience different

attenuation.
2.​ Creates intersymbol interference as delayed signals overlap with subsequent
symbols.
3.​ Degrades error performance more severely for higher-order modulation schemes.
4.​ Mitigation techniques: equalization, OFDM, diversity reception, adaptive modulation.

Q165: Explain the impact of carrier frequency offset on BPSK and QPSK:

1.​ Causes phase rotation over time; degrades constellation integrity.

2.​ QPSK more sensitive than BPSK; smaller phase decision regions.
3.​ Performance degradation accelerates with offset magnitude and symbol duration.
4.​ Recovery techniques: phase-locked loops, pilot symbols, frequency estimators.

Q166: Explain the impact of pulse shaping on bandwidth and inter-symbol

interference:

1.​ Reduces required bandwidth by smoothing transitions between symbols.

2.​ Nyquist filters (raised cosine) minimize ISI by satisfying zero-crossing criterion.
3.​ Roll-off factor controls trade-off between bandwidth efficiency and ISI immunity.
4.​ Root-raised cosine splits filtering between transmitter and receiver for optimal SNR.

Q167: Explain the significance of error vector magnitude (EVM) in digital modulation:

1.​ Quantifies difference between ideal and actual constellation points; key quality
metric.
2.​ Directly correlates with bit error rate; more sensitive than traditional SNR.
3.​ Captures combined effects of noise, distortion, and impairments.
4.​ Typical requirements: <3% for 64-QAM, <8% for 16-QAM, <17.5% for QPSK.

Q168: Explain the advantages and limitations of using frequency-hopping in BFSK:

1.​ Advantages: Resistance to narrowband interference, security through hopping

pattern, reduced multipath effects.
2.​ Limitations: Synchronization complexity, spectral efficiency loss, frequency
synthesizer requirements.
3.​ Performance depends on hopping rate: fast hopping provides diversity; slow hopping
simplifies implementation.
4.​ Trade-off between processing gain and implementation complexity; requires wider
total bandwidth.
Q169: Compare and contrast the use of binary and non-binary LDPC codes in digital
communication:

1.​ Binary LDPC: Uses bits (GF(2)); simpler implementation; good performance for
moderate error rates.
2.​ Non-binary LDPC: Uses symbols from larger fields (GF(q)); better performance
especially for burst errors.
3.​ Decoding complexity: Binary uses sum-product algorithm; non-binary requires more
complex belief propagation.
4.​ Applications: Binary for general-purpose systems; non-binary for high-reliability
storage and specialized channels.

Q170: How does Shannon entropy influence data compression techniques?

1.​ Defines theoretical minimum bits needed to represent information without loss.
2.​ Guides compression algorithm design by identifying redundancy and information
content.
3.​ Entropy coding (Huffman, arithmetic) assigns shorter codes to more probable
symbols.
4.​ Compression ratio limited by source entropy; approaches entropy as code optimality
increases.

Q171: Explain why CRC (Cyclic Redundancy Check) is widely used in error detection:

1.​ Mathematically robust; detects all burst errors up to CRC length and odd number of
bit errors.
2.​ Computationally efficient; implemented with simple shift registers and XOR
operations.
3.​ Flexible length (8-32 bits) balances overhead with detection capability.
4.​ Standard polynomials optimized for specific error patterns and applications.

Q172: How does the use of feedback shift registers improve the implementation of
cyclic codes?

1.​ Enables efficient hardware implementation with minimal components (registers and
XOR gates).
2.​ Provides systematic encoding by separating message and parity bits.
3.​ Supports both encoding and syndrome calculation with similar circuitry.
4.​ Generates code sequences with predictable mathematical properties at high speed.

I notice you've shared what appears to be a list of academic questions about signal
processing, communication systems, and related topics. Let me help by providing
crisp, 4-point answers to each question. I'll start with the first few questions and can
continue with more if needed.

173. Minimum Hamming Distance concept and its

application in error correction
 1.​ Minimum Hamming distance is the smallest number of bit positions in which
any two codewords differ within a coding scheme.
2.​ For error detection, a code with minimum Hamming distance d can detect up to
(d-1) bit errors.
3.​ For error correction, a code with minimum Hamming distance d can correct up
to ⌊(d-1)/2⌋ bit errors.
4.​ Applications include Reed-Solomon codes in storage media, BCH codes in
satellite communications, and Hamming codes in computer memory systems.

174. Significance of choosing an optimal coding

technique for IoT applications
1.​ Energy efficiency: Optimal coding minimizes transmission power
requirements, extending battery life of IoT devices.
2.​ Bandwidth utilization: Efficient coding techniques reduce data size, enabling
more devices to share limited spectrum.
3.​ Reliability: Proper error correction coding ensures data integrity despite
challenging wireless environments and interference.
4.​ Implementation complexity: IoT devices have limited processing capabilities,
requiring coding schemes with reasonable computational demands.

175. Channel coding improving efficiency of satellite

communication systems
1.​ Overcomes high bit error rates due to long transmission distances and
atmospheric interference.
2.​ Reduces required transmit power, allowing smaller antennas and lower-cost
equipment.
3.​ Enables reliable communication at lower signal-to-noise ratios, maximizing
throughput.
4.​ Adaptive coding schemes can adjust to changing channel conditions,
optimizing performance in variable environments.

176. Real-world applications of Huffman coding in

database compression
1.​ Storage optimization: Reduces database size by encoding frequent values with
shorter bit sequences.
2.​ Improved query performance: Smaller data sizes lead to faster disk reads and
reduced memory requirements.
3.​ Backup efficiency: Compressed databases require less bandwidth and storage
for backup operations.
4.​ Column-oriented databases: Particularly effective when used with run-length
encoding for columns with repetitive values.
177. Aliasing effect with a mathematical example
1.​ Aliasing occurs when a signal is sampled below the Nyquist rate (fs < 2fmax),
causing high-frequency components to appear as lower frequencies.
2.​ Mathematical example: A 7 kHz sine wave sampled at 8 kHz will appear as a 1
kHz sine wave (|7 kHz - 8 kHz| = 1 kHz).
3.​ The aliased frequency can be calculated as |f - n·fs|, where f is the original
frequency, fs is the sampling frequency, and n is chosen to minimize the result.
4.​ Visually, if sin(2π·7000t) is sampled at 8000 Hz, the samples would be
indistinguishable from those of sin(2π·1000t).

178. Importance of modulation in signal processing

1.​ Frequency shifting: Modulation translates baseband signals to higher
frequencies suitable for transmission through specific channels.
2.​ Multiplexing: Different signals can share the same medium by modulating them
onto different carrier frequencies.
3.​ Bandwidth efficiency: Advanced modulation schemes like QAM can transmit
multiple bits per symbol, increasing spectral efficiency.
4.​ Noise immunity: Techniques like spread spectrum modulation provide
resistance to interference and jamming.

I'll continue with the remaining questions, providing crisp 4-point answers for each.

179. Practical limitations of the sampling theorem

1.​ Bandwidth limitations: Real signals are rarely perfectly bandlimited, leading to
unavoidable aliasing.
2.​ Timing jitter: Practical sampling systems have clock imperfections causing
irregular sampling intervals, degrading reconstruction accuracy.
3.​ Quantization error: Practical ADCs have finite resolution, introducing
quantization noise not accounted for in the ideal theorem.
4.​ Anti-aliasing filter imperfections: Practical filters cannot perfectly cut off
frequencies above Nyquist, allowing some aliasing to occur.

180. Relationship between impulse response and

convolution for continuous-time LTI systems
1.​ The output y(t) of an LTI system equals the convolution of the input x(t) with
the system's impulse response h(t).
2.​ Mathematically expressed as y(t) = x(t) * h(t) = ∫₋∞^∞ x(τ)h(t-τ)dτ.
3.​ The impulse response h(t) completely characterizes the input-output behavior
of an LTI system.
4.​ This relationship enables analysis of complex signals by decomposing them
into a sum of scaled and delayed impulses.
181. Z-transform, mathematical representation and
applications
1.​ The Z-transform of a discrete-time signal x[n] is defined as X(z) = ∑₋∞^∞
x[n]z^(-n), where z is a complex variable.
2.​ It transforms difference equations into algebraic equations, similar to how the
Laplace transform handles differential equations.
3.​ Applications include system stability analysis, filter design, and determining
frequency responses via the unit circle evaluation.
4.​ Z-transforms facilitate the analysis of discrete-time systems using transfer
functions and pole-zero plots.

182. Challenges in real-time signal processing and

solutions
1.​ Computational constraints: Solved through optimized algorithms, dedicated
DSP hardware, and parallel processing architectures.
2.​ Latency requirements: Addressed by pipelining techniques, reduced buffer
sizes, and hardware acceleration.
3.​ Power consumption: Mitigated with adaptive processing, dynamic
voltage/frequency scaling, and efficient algorithm implementation.
4.​ Variable data rates: Managed through adaptive filtering, dynamic resource
allocation, and multi-rate processing techniques.

183. Importance of multirate signal processing and

applications
1.​ Computational efficiency: Performing filtering at lower sampling rates reduces
processing requirements.
2.​ Spectral analysis: Enables efficient implementation of filter banks for analysis
of different frequency bands.
3.​ Sample rate conversion: Critical for interfacing systems with different
sampling rates in audio, video, and communication systems.
4.​ Applications include audio/video codecs, software-defined radios, digital TV,
and efficient implementation of high-order filters.

184. Adaptive filters and their importance in modern

communication systems
1.​ An adaptive filter automatically adjusts its parameters based on an algorithm
driven by an error signal.
2.​ Applications include channel equalization to combat ISI in wireless systems
and echo cancellation in voice communications.
 3.​ Enables noise cancellation in varying environments by dynamically modeling
and subtracting noise components.
4.​ Critical for MIMO systems to track time-varying channel characteristics and
maximize throughput.

185. How impulse response determines system

causality
1.​ A causal system's impulse response h(t) equals zero for all t < 0 (no output
before input).
2.​ Mathematically, causality requires h(t) = 0 for t < 0.
3.​ In the frequency domain, causal systems have transfer functions that are
analytic in the right half-plane.
4.​ The ROC (Region of Convergence) for a causal system's transfer function
includes the right half-plane.

186. Obtaining step response from impulse response

1.​ The step response s(t) is the integral of the impulse response h(t): s(t) = ∫₋∞^t
h(τ)dτ.
2.​ In the frequency domain, S(ω) = H(ω)/jω, where H(ω) is the Fourier transform
of h(t).
3.​ For discrete-time systems, s[n] = ∑ ₌₀^n h[k].
4.​ Graphically, the slope of the step response equals the value of the impulse
response at any given time.

187. Convolution integral formula for continuous-time

systems
1.​ The convolution integral is defined as y(t) = ∫₋∞^∞ x(τ)h(t-τ)dτ.
2.​ It represents the superposition of infinitesimal impulse responses weighted by
the input signal.
3.​ For causal systems, the limits become y(t) = ∫₀^t x(τ)h(t-τ)dτ with input x(t)
applied at t=0.
4.​ The convolution integral implements the fundamental input-output relationship
of LTI systems.

188. Difference between convolution integral and

convolution sum
1.​ Convolution integral (continuous-time): y(t) = ∫₋∞^∞ x(τ)h(t-τ)dτ uses integration
for continuous signals.
2.​ Convolution sum (discrete-time): y[n] = ∑ ₌₋∞^∞ x[k]h[n-k] uses summation for
discrete signals.
 3.​ Example: Filtering an audio signal (continuous) uses the integral while
processing digital samples uses the sum.
4.​ Both operations maintain the fundamental properties of linearity,
time-invariance, and associativity.

189. Convolution of two rectangular pulse signals

1.​ Defining rect(t) as 1 for |t|≤0.5 and 0 elsewhere, rect(t)*rect(t) yields a triangular
pulse tri(t).
2.​ The result has duration equal to the sum of the durations of the individual
pulses.
3.​ Mathematically: tri(t) = {1-|t| for |t|≤1, 0 elsewhere}, representing the overlap
area as one pulse slides past the other.
4.​ This demonstrates the "smoothing" effect of convolution, relevant in pulse
shaping and signal filtering.

190. Correlation and its mathematical expression for CT

and DT signals
1.​ Continuous-time correlation: Rxy(τ) = ∫₋∞^∞ x(t)y(t+τ)dt measures similarity
between signals x(t) and y(t).
2.​ Discrete-time correlation: Rxy[m] = ∑ₙ₌₋∞^∞ x[n]y[n+m] for discrete signals.
3.​ Auto-correlation (x=y) reveals periodicities and is maximum at zero lag for
energy signals.
4.​ Cross-correlation measures similarity between different signals, used in
pattern recognition and signal detection.

191. How satellite transponders work in communication

systems
1.​ Transponders receive signals from Earth stations, amplify them, and shift their
frequency (typically down-convert).
2.​ They function as "bent-pipe" relays, operating on specific frequency bands (C,
Ku, Ka) with defined bandwidths.
3.​ Multiple transponders share satellite resources through frequency division to
handle multiple channels.
4.​ Modern transponders incorporate digital processing for signal regeneration,
error correction, and switching capabilities.

192. Advantages and disadvantages of LEO, MEO, and

GEO satellites
1.​ LEO (Low Earth Orbit): Low latency (30ms) and power requirements, but
requires large constellations and has complex handover.
 2.​ MEO (Medium Earth Orbit): Moderate coverage and latency (100ms), balanced
system complexity, used primarily for navigation.
3.​ GEO (Geostationary Orbit): Constant position provides wide coverage with few
satellites, but high latency (250ms) and power needs.
4.​ Each orbit type serves different applications: LEO for low-latency
communications, MEO for navigation, GEO for broadcasting and fixed
communications.

193. Importance of interference management in

multi-user communication
1.​ Spectrum efficiency: Proper interference management maximizes the number
of users sharing limited frequency resources.
2.​ Quality of service: Controlling interference ensures reliable data rates and low
error probabilities for all users.
3.​ Network capacity: Advanced interference management techniques like MIMO
and beamforming significantly increase system capacity.
4.​ Energy efficiency: Effective interference mitigation reduces required transmit
power, extending battery life in mobile devices.

194. Handover process in GSM and CDMA networks

1.​ GSM uses hard handovers ("break-before-make") where connection to the
original cell is broken before connecting to the new cell.
2.​ CDMA employs soft handovers ("make-before-break") where the mobile
connects to multiple base stations simultaneously.
3.​ CDMA's soft handover provides better call quality and reduces the "ping-pong
effect" but requires more network resources.
4.​ GSM handovers are simpler to implement but cause momentary service
interruptions and higher drop rates in high-mobility scenarios.

195. Multiple access techniques in cellular networks

1.​ FDMA (Frequency Division): Allocates unique frequency bands to users, used
in analog cellular systems, simple but spectrally inefficient.
2.​ TDMA (Time Division): Assigns unique time slots to users on shared
frequencies, improved efficiency, used in GSM.
3.​ CDMA (Code Division): Users share time and frequency but use unique
spreading codes, higher capacity and security, used in 3G.
4.​ OFDMA (Orthogonal FDMA): Combines FDMA and TDMA principles with
orthogonal subcarriers, highly efficient, used in 4G/5G.

196. Impact of duplexing techniques on cellular

communication performance
 1.​ FDD (Frequency Division Duplexing): Uses separate frequencies for
uplink/downlink, enabling simultaneous transmission but requiring more
spectrum.
2.​ TDD (Time Division Duplexing): Alternates between uplink/downlink on same
frequency, more spectrum-efficient but introduces latency.
3.​ TDD allows asymmetric bandwidth allocation, beneficial for data-centric
services with uneven traffic patterns.
4.​ FDD provides lower latency and simpler interference management, while TDD
offers better adaptation to traffic asymmetry.

197. Cell splitting improving network efficiency

1.​ Increases capacity by reusing frequencies across smaller cells, improving
spectrum utilization per unit area.
2.​ Reduces transmit power requirements, extending battery life and reducing
interference.
3.​ Enables more targeted coverage, improving service in high-demand areas and
reducing dead zones.
4.​ Introduces challenges including increased handover complexity,
synchronization requirements, and backhaul infrastructure needs.

198. Case study of multi-user detection improving

mobile communication
1.​ CDMA systems in dense urban environments saw 30-40% capacity increases
through successive interference cancellation techniques.
2.​ 3G UMTS deployments used parallel interference cancellation to effectively
double uplink capacity in high-traffic areas.
3.​ LTE-Advanced implementations with minimum mean square error (MMSE)
receivers achieved up to 3x improvement in cell-edge performance.
4.​ Massive MIMO deployments in commercial 5G networks demonstrated 5-10x
capacity gains through spatial multi-user detection.

199. How 5G revolutionizes multi-user communication

1.​ Massive MIMO technology enables spatial multiplexing of dozens of users
simultaneously on the same frequency resources.
2.​ Millimeter wave spectrum provides vast bandwidth, supporting multi-gigabit
speeds across many concurrent users.
3.​ Network slicing creates virtually independent networks tailored to specific
service requirements on shared infrastructure.
4.​ Advanced beamforming techniques focus energy precisely toward users,
minimizing interference and maximizing spectral efficiency.
200. Approach for designing a satellite network for
global broadband access
1.​ Hybrid constellation combining LEO satellites (for low latency) with GEO
satellites (for coverage in remote areas).
2.​ Inter-satellite links to minimize ground station requirements and provide
resilient connectivity paths.
3.​ Adaptive coding and modulation to optimize throughput despite varying
channel conditions and interference.
4.​ Software-defined networking architecture enabling dynamic resource
allocation based on geographic demand patterns.