What are the differences between analog and digital communication?

Isdigital communication
better than analog? If yes, why?
Analog communication uses signals whose amplitude varies continuously with time whereas in
digital communication, the signals have only 2 types of amplitudes either high (1) or low (0). Analog
communication has some drawbacks such as noise, interference, and signal degradation. Digital
communication is used in the first place to overcome these drawbacks of analog communication.
Digital communication is considered better over analogcommunication mainly because of its
capability of reducing noise and interference. But one more reason is that discerning exact analog
signals is more difficult than discerning discrete values.

What are the different source, sink and data types in GNU radio?
Data types: Every input and output port on a block will have a data type associated with it. The data
type is identified by the color of the input andoutput port. The different data types in GNU radio are
complex, short, int,float, byte.
Sources: Produce a finite or infinite sequence of values. There are three typesof sources.
Signal source- can produce a sine wave or triangle wave or many such signals.Vector source- takes a
set of samples and convert them to a waveform.
File source- Reads data from a file and converts back to a signal.
Sinks: Consumes samples, potentially output/display them.
There are fourtypes of sinks Time/frequency sink
Hardware sink- consumes samples and outputs them as audio or radio signalsthat are transmitted
through hardware systems.
File sink- used to write samples to a file for later analysis.
Null sink- consumes samples but does not do anything with them. Comes inhandy while performing
debugging operations.

Question 1: What are the key advantages of digital communication over analog communication?
Answer:
Noise Immunity: Digital signals can be more resilient to noise compared to analog signals due to the
discrete nature of digital encoding.
Multiplexing: Digital signals allow for easier multiplexing, enabling multiple signals to be transmitted
simultaneously over the same channel.
Error Detection and Correction: Digital communication systems can employ sophisticated error
detection and correction techniques, ensuring data integrity.
Compression: Digital signals can be compressed efficiently, allowing for more data to be transmitted
in a given bandwidth.
Compatibility with Computers: Digital signals can be easily processed and manipulated by computers,
facilitating integration with digital systems and networks.
Question 2: What are the basic components of a digital communication system?
Answer:
Transmitter: Converts information into a digital signal suitable for transmission over a
communication channel.
Channel: Medium through which the digital signal is transmitted, which could be wired or wireless.
Receiver: Receives the transmitted digital signal and converts it back into the original information.
Codec: Encodes and decodes digital signals for efficient transmission and reception.
Modulation/Demodulation: Modulation prepares the digital signal for transmission, while
demodulation extracts the original information from the received signals.
Question 2: How does GNU Radio handle input and output in digital communication systems?
Answer:
Input: GNU Radio supports various input sources such as audio devices, network streams, and file
inputs to receive digital signals.
Output: Processed signals can be outputted to various devices or mediums, including audio devices,
network streams, files, or even hardware interfaces.
Buffering: GNU Radio employs buffering techniques to handle data flow efficiently between input
and output devices, preventing overflow or underflow.
Real-time Processing: GNU Radio can process input signals in real-time, enabling applications in live
communication systems.
Stream Synchronization: GNU Radio ensures synchronization between input and output streams to
maintain data integrity and temporal coherence in communication systems.

Question 1: What are some advanced blocks in GNU Radio commonly used for digital
communication purposes?
Answer:
Symbol Sync: Synchronizes receiver timing with the transmitted symbols to facilitate accurate
demodulation.
Costas Loop: Used for carrier recovery in phase-shift keying (PSK) modulation schemes.
Frequency Sync: Adjusts receiver frequency to match the transmitted carrier frequency for coherent
demodulation.
Timing Recovery: Recovers the clock timing of the transmitted symbols to enable proper
demodulation.
Equalizer: Compensates for channel distortion and interference to improve the quality of received
signals

Question 2: What are some common digital modulation schemes used in digital communication
systems?
Answer:
Amplitude Shift Keying (ASK): ASK modulates the amplitude of a carrier signal to represent digital
symbols, typically binary ones and zeros.
Frequency Shift Keying (FSK): FSK modulates the frequency of a carrier signal to convey digital
symbols, with different frequencies representing different bits.
Phase Shift Keying (PSK): PSK modulates the phase of a carrier signal to encode digital symbols, with
different phase shifts representing different bits.
Quadrature Amplitude Modulation (QAM): QAM combines ASK and PSK techniques to modulate
both amplitude and phase of a carrier signal, allowing for higher data rates.
Orthogonal Frequency Division Multiplexing (OFDM): OFDM divides the available bandwidth into
multiple orthogonal subcarriers, each carrying data symbols, enabling robust communication in
frequency-selective channels.

How are repetition codes implemented and applied in digital communication systems, and what
are some practical considerations?
Answer:
Encoding and Decoding: Repetition codes are implemented by encoding each data bit multiple times
during transmission and decoding the repetitions at the receiver to detect and correct errors.
Decoding involves taking the majority vote among the repetitions to determine the corrected data
bit.
Error Detection and Correction: Repetition codes provide error detection and correction capability,
allowing the receiver to detect and correct transmission errors based on the majority vote among
the repetitions of each data bit. The correction process assumes that transmission errors are more
likely to cause single-bit errors than multiple-bit errors.
Overhead: Repetition codes incur additional overhead due to the repetition of each data bit,
increasing the size of the transmitted message and reducing the effective data rate and spectral
efficiency of the communication system, particularly for higher repetition factors.
Error Correction Limitations: Repetition codes have limitations in error correction capability, as they
can only correct errors if the majority of repetitions agree. If the number of errors exceeds the
correction capability of the code, the receiver may not be able to correct the errors, leading to error
propagation and degradation in system performance.
Performance Evaluation: Repetition code performance is evaluated using metrics such as error
detection rate, error correction rate, false positive rate, and throughput, providing insights into error
correction effectiveness and overhead impact on system performance under varying channel
conditions and noise levels.

How is the (7,4) Hamming code applied in GNU Radio for error detection and correction, and what
are some practical considerations?
Answer:
Encoding and Decoding: The (7,4) Hamming code in GNU Radio encodes blocks of four data bits into
seven-bit codewords using linear combinations specified by the generator matrix, and decodes
received codewords to detect and correct single-bit errors using the parity check matrix and
syndrome decoding techniques.
Implementation Efficiency: The (7,4) Hamming code implementation in GNU Radio should be
optimized for efficiency, minimizing computational complexity and overhead while maximizing error
correction capability and system reliability.
Parity Check Matrix Design: The design of the parity check matrix for the (7,4) Hamming code should
ensure that the codewords are linearly independent and have sufficient Hamming distance to detect
and correct single-bit errors effectively, balancing error correction capability with redundancy and
computational complexity considerations.
Syndrome Decoding Algorithms: The (7,4) Hamming code in GNU Radio uses syndrome decoding
algorithms to correct single-bit errors based on the computed syndrome, which represents the
difference between the received codeword and the closest valid codeword in the code space. The
choice of decoding algorithm impacts error correction performance and computational complexity.
Performance Optimization: The performance of the (7,4) Hamming code in GNU Radio is optimized
by adapting system parameters, selecting appropriate decoding algorithms, and managing overhead
to maximize error correction effectiveness and minimize impact on system performance under
varying channel conditions and noise levels.
Question 1: Explain the concept of modulation in digital communication. Discuss the differences
between amplitude modulation (AM) and frequency modulation (FM) techniques. Provide real-
world examples where each modulation technique finds its application.
Solution:
Modulation is the process of varying a carrier wave's properties, such as amplitude, frequency, or
phase, in accordance with the signal to be transmitted.
Amplitude Modulation (AM) involves varying the amplitude of the carrier signal in proportion to the
waveform being sent. It is commonly used in broadcast radio transmissions.
Frequency Modulation (FM) varies the frequency of the carrier wave with the amplitude of the input
signal. It is widely used in radio broadcasting and two-way radio communication.
Real-world examples:
AM: AM radio broadcasting, where voice or music signals modulate the amplitude of the carrier
wave. FM: FM radio broadcasting, where voice or music signals modulate the frequency of the
carrier wave. Also, mobile phone communication utilizes FM techniques for clearer voice
transmission.
Question 1: Explain the role of Python in GNU Radio and its significance in digital communication
systems. Discuss how Python scripts can be utilized to control and automate signal processing tasks
in GNU Radio. Provide examples of Python scripts used for implementing signal processing
algorithms inGNU Radio.
Solution:
Python is a scripting language commonly used in GNU Radio for controlling and automating signal
processing tasks.
Python scripts in GNU Radio can interface with the GNU Radio Companion (GRC) to design and
execute signal processing flowgraphs, allowing for flexible and customizable signal processing chains.
Python scripts can be utilized to implement complex signal processing algorithms, such as digital
filters, modulation/demodulation schemes, and channel coding techniques, by leveraging existing
GNU Radio blocks or custom Python functions.
Examples of Python scripts in GNU Radio include scripts for implementing software-defined radios
(SDRs), performing real-time spectrum analysis, and simulating digital communication systems.
Explain the key characteristics of Amplitude Shift Keying (ASK) as a linear modulation method.
Solution
Sensitivity to Noise: ASK is susceptible to noise due to its reliance on amplitude variations.
Bandwidth Efficiency: It typically requires more bandwidth compared to othermodulation
techniques.
Implementation Simplicity: ASK implementations are simple and cost-effective.
Power Efficiency: Can be power-efficient with proper amplifier usage.
Data Rate Flexibility: Supports various data rates based on modulation parameters.

Explain the fundamentals of digital modulation in five points.

Solution
Digital Data Representation: Digital modulation involves encoding digital data intodiscrete
symbols, typically binary digits (0s and 1s).
Carrier Signal Modulation: The digital symbols are modulated onto a carrier signal using
techniques like ASK, FSK, PSK, or QAM.
Symbol Mapping: Each digital symbol is mapped onto the carrier signal using predefined schemes,
altering parameters like amplitude, frequency, or phase.
Bandwidth Efficiency and Robustness: Digital modulation techniques aim for efficient use of
bandwidth and robustness against noise and interference.
Demodulation at Receiver: At the receiver, the modulated signal is demodulated toretrieve the
original digital data, involving the reversal of the modulation process.
Explain five properties of Gaussian random variables in the context of detection theory.
Solution
Mean and Variance: Gaussian random variables are defined by their mean (μ) and variance (σ^2),
representing their central tendency and spread, respectively.
Central Limit Theorem: Gaussian distributions emerge due to the Central Limit Theorem, where the
sum of independent random variables tends towards a Gaussian distribution.
Probability Density Function (PDF): Gaussian random variables follow a bell-shapedcurve with a
symmetric PDF around the mean.
Independence of Real and Imaginary Parts: In complex Gaussian random variables, the real and
imaginary parts are independent Gaussian distributions.
Optimality in Maximum Likelihood Detection: Gaussian assumptions lead to optimal solutions in
maximum likelihood detection problems, simplifying detection strategies.
Question 2:
Consider a real-valued random variable X that is Uniformly distributed between
-1 and 1 . Determine the value of b0 - b1 for the optimal 1-bit quantizer for Xthaat minimizes the
mean squared error , mapping X to the points {b0 , b1} where b1> b0.
Solution:
For a uniformly distributed random variable between -1 and1, the optimal 1-bitquantizer divides the
range into two equal intervals. The decision boundary b0 separates the interval [-1 , b0] from [b0,1],
and b1 separate [-1 , b1 ] from [b1 ,1], where b1> b0.
that they partition the range into two equal intervals. Since the range is 2 unitswide, each interval
will be 1 unit wide.
Therefore, b1 - b0=2.Answer:
b1 - b0 = 2
A communication system employs a (7,4) binary Hamming code over a binary
symmetric channel with a bit flip probability p, where 0<p<0.5. Compute the
probability that a single codeword can be decoded without any errors.
Solution:
In a (7,4) binary Hamming code, there are 7 bits in each codeword, of which 4are
information bits and 3 are parity bits. The Hamming distance between anytwo
codewords is at least 3, meaning that the code can detect up to 2 errors and correct a
single error.
The probability that a single codeword can be decoded without any errors is the
probability that no more than one bit is flipped during transmission. Since the bit flip
probability is p, the probability of no error occurring is (1−p)^7. This is because for each
bit, there is a probability (1−p) that it remains unchanged.
The probability that a single codeword can be decoded without any errors is (1−p)^7.

Explain the detection and optimal decision process for On-Off signaling in Additive
White Gaussian Noise (AWGN) channel.
Solution
Signal Representation: On-Off signaling toggles between transmission states in an
AWGN channel.
Hypotheses: Two hypotheses are formulated: H0 for no transmission and H1 for
transmission.
Optimal Detector: Design a detector to minimize error probability.
Decision Rule: Utilize a threshold-based decision rule to distinguish between
transmission and no transmission based on received signal statistics.
Performance Evaluation: Evaluate detector performance in terms of error
probabilities, adjusting threshold for desired trade-offs.
Describe the process of constructing and visualizing constellations using GNU Radio.
Solution
Signal Generation: Use GNU Radio to create a flowgraph generating the digital
modulation signal.
Symbol Mapping: Map digital bits to symbols in the modulation constellation using
the Map block.
Adding Noise: Introduce noise using the Noise Source block to simulate real-world
channel conditions.
Visualization: Utilize the Constellation Sink block to visually represent the constellation
diagram.
Analysis: Analyze the constellation to evaluate modulation scheme performance under
different conditions.

What is the relationship between symbol energy (Es) and bit energy (Eb) ? Also
calculatethe ratio of Es and Eb for QAM-16.
Solution
The relationship between the energy per symbol Es and the energy per bit Eb is:
Es=k*Eb
Where k is the number of bits per symbol.
For QAM 16 the value of k is 4 because 16=2^n here the value of n is 4 So, the ratio of
symbol energy Es to bit energy Eb is :
Es/Eb=4
So the ratio is 4

Given X1,X2,…X10are i.i.d. real-valued random variables that are Gaussian with mean
0 andunit variance. Let Y=2(X1+X2+…X10) find the variance of Y ?
Solution
Given Y=2(X1+X2+…+X10), we can compute its variance as follows:

Var(Y)=Var(2(X1+X2+…+X10))

Since the Xi are i.i.d. and have unit variance, the variance of their sum is simply the
sum of
their variances. Hence:

Var(Y)=⋅(2^2)*Var(X1+X2+…+X10)

Var(Y)=4⋅Var(X1+X2+…+X10)
Since Xi
are i.i.d., we can apply the property that the variance of the sum of
independent
random variables is the sum of their variances. Therefore:

Var(Y)=4⋅(Var(X1)+Var(X2)+…+Var(X10))

Given that the variance of eachXi is 1, we have:

Var(Y)=4⋅(1+1+…+1)=4⋅10=40

The amplitude of a signal used for binary digital transmission over an AWGN channel
is doubled without any other parameters changing .Can you briefly explain how it
impacts on the effective SNR.
Solution
SNR is calculated as the ratio of signal power to noise power.
Doubling the amplitude of the signal increases the signal power by a factor of 4 (since
poweris proportional to the square of the amplitude).
Since the noise power remains unchanged, the SNR increases by the same factor of 4.
Now, the relationship between changes in SNR and changes in decibels (dB) is given by:
Change in dB=10*log10 (new SNR / old SNR)
In this case, the new SNR is 4 times the old SNR.
Change in dB=10*log10 (4*old SNR / old SNR)
=10*log(4) = 6.02 dB

Rounding off, the change in SNR is approximately 6 dB.

Explain the process of simulating an end-to-end digital communication system in

GNU Radio.
Solution
Simulating an end-to-end digital communication system in GNU Radio involves:
Designing the flowgraph, representing signal processing blocks.
Configuring each block with relevant parameters.
Executing the flowgraph for simulation.
Analyzing simulation results.
Validating and refining the simulation as needed.

Explain the concept of maximum likelihood delay estimate for a single symbol in GNU
Radio.
Solution
In GNU Radio, the maximum likelihood delay estimate for a single symbol refers to the
process of estimating the time delay or phase offset between the received signal and
the locally generated reference signal. This estimation is crucial in digital
communication systems for synchronization purposes.
It involves the following steps:
Signal Acquisition
Acquire the received signal through an ADC.
Reference Signal Generation:
Generate a known reference signal synchronized with the received signal.
Delay Estimation:
Compare received signal with reference signal at various delays or phase offsets.
Estimate delay that maximizes likelihood of signal match.
Maximum Likelihood Algorithm:
Employ algorithms like correlation, likelihood ratio tests, or maximum likelihood
estimation.
Implementation in GNU Radio:
Use signal processing blocks such as correlators, matched filters, and phase estimator

How can errors be minimized in communication?

*Proofreading: Double-check written communication for spelling and grammar errors.
*Clarity: Use simple language and avoid jargon to reduce the risk of misinterpretation.
*Verification: Confirm information before relaying it to ensure accuracy.
*Feedback loop: Encourage recipients to ask questions or seek clarification to catch
errors early.
*Training: Provide communication skills training to employees to enhance accuracy and
effectiveness.

a. Define noise filtering?

b. Explain two common techniques used for noise filtering?

c. Describe the importance of noise filtering in signal processing?

d. Provide an example scenario where noise filtering is crucial?

e. Discuss the limitations of noise filtering technique?

* Noise filtering refers to the process of removing unwanted or irrelevant signals,

known as noise, from a signal.
* Two common techniques for noise filtering are:

Low-pass filtering, which attenuates high-frequency noise

components. Adaptive filtering, where filter parameters adjust

based on signal characteristics.

* Noise filtering is crucial in signal processing to improve signal quality, enhance

data accuracy, and facilitate better analysis and interpretation.
* In medical imaging, noise filtering is essential to enhance the clarity of
diagnostic images byremoving artifacts and irrelevant signals, aiding accurate
diagnosis.
* Limitations of noise filtering techniques include potential distortion of the
signal, loss of useful information, and challenges in selecting appropriate filter
parameters.

1) What is Quantization in Digital Signal Processing?

*Quantization is the process of approximating continuous values with discrete values.

*It involves dividing the range of a continuous signal into a finite number of intervals.
*Quantization introduces quantization error, which is the difference between the
original continuous signal and its quantized representation.
*The number of quantization levels determines the resolution of the quantized signal.
*In digital signal processing, quantization is essential for converting analog signals
into digital format for processing and transmission.
*Quantization in digital signal processing refers to the approximation of continuous
values with discrete values. It involves dividing the range of a continuous signal into
intervals and introducing quantization error. The resolution of the quantized signal
depends on the number of quantization levels. This process is crucial for converting
analog signals into digital format for processing and transmission.

2) Discuss the Effects of Quantization on Signal Quality.

*Quantization introduces quantization error, which can degrade signal quality.

*Increasing the number of quantization levels reduces quantization error and
improves signal accuracy.
*However, increasing the number of quantization levels also increases the required
storage or transmission capacity.
*Quantization noise, a type of distortion, can affect the fidelity of the signal.
*Properly choosing the number of quantization levels is crucial to balance between
signal accuracy and resource consumption.
*Quantization affects signal quality by introducing quantization error, which can
degrade accuracy. More quantization levels reduce error but increase resource
requirements. Quantization noise, a
 form of distortion, can further impact signal fidelity. Balancing the number of quantization levels is
crucial for optimizing signal quality while managing resource consumption.

What is channel equalization, and why is it important in communication systems?

Solution
Channel equalization is a signal processing technique used to mitigate the effects of channel
distortion in communication systems.
It is important because
It aims to reverse or compensate for distortion introduced by the channel, improving the accuracy
and reliability of data transmission.
Equalization employs filters or adaptive algorithms to restore the transmitted signal to its original
form at the receiver.
By doing so, it enhances overall system performance by minimizing errors caused by channel
distortion.
Channel equalization is essential for robust and efficient communication over noisy and
distorted channels.
An AWGN channel transforms a real input X to Y using the relationship Y=3X+W where W is a real
additive white Gaussian noise process. X^=kY is the zero-forcing estimate at the receiver. Find the
value of k
Solution
Given

X^=kY

Where:

X^ is the estimated transmitted signal,

is the received signal,Y

is the scaling factor.k

X Y
Given the relationship between and in the AWGN channel as Y=3X+W, we can substitute

it into the equation for the zero-forcing estimate:

X^=k(3X+W)

To perform zero-forcing equalization, we want to eliminate the effect of the channel, which
X^
means we want to eliminate the term involving W. In other words, we want to be equal t
when there
X is no noise.

To achieve this, we set k=1/3

X^=1/3(3X+W)

Thus, the value of k is 1/3

Consider an Orthogonal Frequency Division Multiplexing (OFDM) system operating in the
presence of dispersive channels. The system employs 64 subcarriers and uses a cyclic prefix
(CP) of length 16 samples. The channel has an impulse response given by h[n]=δ[n]+0.5δ[n−1],
where δ[n] denotes the Dirac delta function.

Calculate the total number of samples per OFDM symbol, and determine the number of
degrees of freedom lost due to the CP.
Solution
Total samples per symbol = Number of subcarriers + Length of CP = 64 + 16 = 80 samples.Number of
CP samples = Length of CP = 16.
Number of degrees of freedom lost = Number of CP samples / Total samples per symbol = 16
/ 80 = 0.2.
Therefore, the number of degrees of freedom lost due to the cyclic prefix is 0.2, orequivalently,
20% of the total number of samples per OFDM symbol.

Consider a communication system that uses a parity check code with a block length of 12 bits.
Determine the number of parity bits required for this code to detect and correct single-bit errors.
Explain the encoding process for the parity check code with a block length of 12 bits. Provide
an example of encoding a message.
If during transmission a code word of this parity check code experiences a single-bit error, explain
how the receiver can detect and correct this error using parity bits.
Solution:
For a parity check code with a block length of 12 bits, we can use the formula (2^m ≥ n + m
+ 1) to determine the number of parity bits needed to detect and correct single-bit errors. Given n
= 12, where n is the number of data bits, we solve for m:
(2^m ≥ n + m + 1)
By trial and error, we find that m = 4 satisfies the inequality:
[2^4 ≥ 12 + 4 + 1]
[16 ≥ 17]
Therefore, the number of parity bits required for this code to detect and correct single-bit errors is
4.
The encoding process for the parity check code involves adding parity bits to the data bits such that
the total number of bits in the code word has even parity. An example of encodinga message with a
block length of 12 bits is as follows:
Original message: 101010101010
Add parity bits to achieve even parity: 1010101P1010 Where 'P' is the calculated parity bit.
If during transmission a code word of this parity check code experiences a single-bit error, the
receiver can detect and correct this error using parity bits by checking whether the parity of received
code word is even. If the parity is not even, an error is detected. By comparing the received code word
with the valid code words generated using parity check bits, the receiver can identify and correct the
erroneous bit position by flipping it to restore even parity.

Consider a communication system that employs a repetition code with a repetition factor of 5.
Calculate the code rate of this repetition code.
Explain the encoding process for the repetition code with a repetition factor of 5. Provide an
example of encoding a message.
Discuss the trade-offs associated with using repetition codes in terms of error detection and
correction capabilities, redundancy, and code rate.

Solution:
The code rate of a repetition code can be calculated as the ratio of the number of information bits to
the total number of bits in the code word. Since each bit is repeated 5 times, the code rate is 1/5.
The encoding process for the repetition code involves replicating each data bit multiple times to
create the code word. An example of encoding a message using a repetition factor of 5 is as follows:
Original message: 1011
Encoded codeword: 111111111100000000001111
Repetition codes provide simple encoding and decoding processes, making them easy to implement.
They are effective at detecting and correcting errors when the majority of bits in a codeword are
correct. However, repetition codes suffer from poor efficiency (low code rate)as they require
redundant bits. Although they can correct errors, they are more suited for error detection.
Additionally, repetition codes are inefficient in terms of bandwidth utilization, as they transmit
multiple copies of the same data bit. Therefore, while repetition codes offer simplicity and error
detection capabilities, they come at the cost of low efficiency and high redundancy.

How does GNU Radio handle input and output in digital communication systems?
Answer:
Input: GNU Radio supports various input sources such as audio devices, network streams, and file
inputs to receive digital signals.
Output: Processed signals can be outputted to various devices or mediums, including audio devices,
network streams, files, or even hardware interfaces.
Buffering: GNU Radio employs buffering techniques to handle data flow efficiently between input
and output devices, preventing overflow or underflow.
Real-time Processing: GNU Radio can process input signals in real-time, enabling applications in live
communication systems.
Stream Synchronization: GNU Radio ensures synchronization between input and output streams to
maintain data integrity and temporal coherence in communication systems.

What is Amplitude Shift Keying (ASK), and how does it encode digital information?
Answer: Amplitude Shift Keying (ASK) is a modulation technique in which the amplitude of the
carrier signal is varied to represent digital data. In ASK, the binary information is encoded by shifting
the amplitude of the carrier signal between two or more predefined levels. The different amplitude
levels correspond to different binary symbols (e.g., 0 and 1). The receiver detects the amplitude of the
received signal and maps it to the corresponding binary value. ASK is a simple modulation scheme,
but it is susceptible to noise and interference, making it less commonly used in modern digital
communication systems compared to other modulation techniques like PSK and QAM.

Q14: What is Phase Shift Keying (PSK), and how does it differ from other modulation schemes?
Answer: Phase Shift Keying (PSK) is a digital modulation technique in which the phase of the carrier
signal is varied to represent the digital data. In PSK, the binary information is encoded by shifting the
phase of the carrier signal among a set of predefined phase angles. The different phase angles
correspond to different binary symbols or combinations of bits. The receiver detects the phase of the
received signal and maps it to the corresponding binary value(s). PSK is widely used in various
digital communication systems due to its constant envelope, which allows for efficient amplification
and reduces the need for highly linear power amplifiers. PSK differs from other modulation schemes
like ASK and QAM in that it modulates the phase of the carrier signal rather than its amplitude or a
combination of amplitude and phase.

Q15: What is Quadrature Amplitude Modulation (QAM), and how does it improve spectral
efficiency?
Answer: Quadrature Amplitude Modulation (QAM) is a digital modulation technique that combines
both amplitude and phase modulation. In QAM, the amplitude and phase of the carrier signal are
varied to represent different combinations of binary bits. The modulated signal is a complex-valued
signal with two components: the in-phase (I) component and the quadrature (Q) component. Each
combination of I and Q values represents a unique signal point or symbol in a two-dimensional
constellation diagram. QAM allows for higher-order modulation schemes, such as 16-QAM, 64-
QAM, or even 256-QAM, which encode more bits per symbol, resulting in improved spectral
efficiency compared to modulation schemes like PSK or ASK.

Q16: What is Frequency Shift Keying (FSK), and what are its applications?
Answer: Frequency Shift Keying (FSK) is a digital modulation technique in which the frequency of
the carrier signal is varied to represent the digital data. In FSK, the binary information is encoded by
shifting the frequency of the carrier signal between two or more predefined frequencies. The different
frequencies correspond to different binary symbols (e.g., 0 and 1). The receiver detects the frequency
of the received signal and maps it to the corresponding binary value. FSK is commonly used in
applications where low-cost and low-complexity implementations are required, such as in wireless
sensor networks, telemetry systems, and low-speed data communication. FSK is particularly suitable
for non-coherent detection, which simplifies the receiver design and makes it robust to frequency
offsets and phase variations. However, FSK is generally less spectrally efficient compared to other
modulation schemes like PSK and QAM.

Q17. What is a raised cosine pulse, and why is it important in digital communications?
Answer: A raised cosine pulse is a specific waveform used in digital communications to shape the
transmitted signal and minimize intersymbol interference (ISI). It is a pulse shaping filter designed to
have a continuous- time Fourier transform that is zero at certain frequencies, thereby reducing the
spectral sidelobe levels and confining most of the signal energy within a limited bandwidth.
The raised cosine pulse is important in digital communications for several reasons:
Spectral efficiency: By limiting the signal energy within a specific bandwidth, the raised cosine pulse
enables more efficient use of the available frequency spectrum, allowing for higher data rates or
denser channel spacing in bandwidth-constrained applications.

Intersymbol interference mitigation: The raised cosine pulse is designed to have zero crossings at
specific time instants, which helps minimize the interference between adjacent symbols, reducing
intersymbol interference (ISI) and improving the reliability of data transmission.

Controlled spectral characteristics: The raised cosine pulse has well-defined spectral properties, with
the ability to control the rolloff factor, which determines the tradeoff between the occupied bandwidth
and the extent of ISI mitigation.
Explain digital modulation techniques and their applications in communication systems.
Answer:
Definition: Digital modulation involves modifying a carrier wave's key parameters (amplitude,
frequency, or phase) to encode digital data.
Types of Digital Modulation:
Amplitude Shift Keying (ASK): Uses different amplitudes to represent binary symbols (0s and 1s).
Common in optical communication systems.
Frequency Shift Keying (FSK): Changes the carrier frequency to encode digital data. Widely used in
wireless communication.
Phase Shift Keying (PSK): Alters the carrier phase to represent digital bits. Popular in satellite
communication and WiFi.
Advantages: Digital modulation provides robustness against noise and interference, allows for
efficient use of bandwidth, and facilitates error detection and correction.
Applications:
Wireless Communication: Used in mobile networks (GSM, LTE), WiFi, and satellite communication.
Digital Broadcasting: Utilized in digital radio (DAB) and television (DVB).

A 256 point OFDM based system employs QPSK on 128 subcarriers and QAM-16 on 128
subcarriers. The cyclic prefix length is 10. Thesymbol rate is 1,000 symbols per second. What is the
effective bit rate
Answer:
A single OFDM frame consists of 256 + 10 = 266 symbols.
Within this, QPSK gives us 128 × 2 = 256 bits,
while QAM-16 gives us 128×4 = 512 bits.
Therefore, the effective bit rate is 1000×(256 + 512)/266 = 2, 887.2 bits per second. Range [2886,
2890].

The rate of a parity check code that takes a block of 5 information bits and appends one parit bit
to it is

To calculate the rate of a parity check code, you need to consider the number of information bits and
the total number of bits transmitted, including both information bits and parity bits.
In this case, the code appends one parity bit to a block of 5 information bits.
The rate R of a code is given by:
=Total Number of BitsNumber of Information Bits
Given:
Number of information bits = 5
Total number of bits = 5 (information bits) + 1 (parity bit) = 6
So, the rate R is: 5/6
The generator matrix of a binary linear block code, where the information bits are pre-multiplied
by a row matrix, has 4 rows and 10 columns. Its parity check matrix has how many no of rows ?

To find the number of rows in the parity check matrix, we can use the fact that the generator
matrix has 4 rows and 10 columns and that the product of the generator and parity check
matrices results in the identity matrix.

The dimensions of the generator matrix are 4×10, meaning it can generate 4-dimensional
codewords from 10-dimensional input vectors.

The parity check matrix, denoted by H, will have dimensions such that H×G=0, where 00 is
the zero matrix of appropriate size and G is the generator matrix.

Since the product of H and G results in the zero matrix, the number of columns in H must
match the number of rows in G, which is 10. Also, to ensure the product results in a zero
matrix, the number of rows in H must be such that when H is multiplied by G, the result is a
4×4 identity matrix.

Thus, the parity check matrix H will have 10−4=6 rows. So, the parity check matrix has 6 rows.

A (7,4) binary linear block code would have how many unique codewords.
In binary symmetric channel is one where the noise added to a bit is typically
modeled by which operation
A parity check code takes in 3 information bits and appends one parity bit at the end.
The (n,k) representation of this code is
The parity check matrix of a binary linear block code is known to Be [1, 1, 1, 1]. This
code is:

Solution

To calculate the number of unique codewords in a (7,4) binary linear block code, we use the
formula:
2^k
where k is the number of information bits. In a (7,4) code, there are 4 information bits.
So, the number of unique codewords is 2^4=16
XOR
(4, 3)
The (4, 3) single parity check code
A communication system employs the (5,1) binary repetition code over a binary symmetric
channel with bit flip probability p, with 0<p<0.5. The effective bit error rate is

To calculate the effective bit error rate (BER) for the (5,1) binary repetition code over a binary
symmetric channel with bit flip probability p, we need to consider all possible combinations
of errors.

In the (5,1) repetition code, a received bit is in error if at least 3 or more of the 5 repetitions
are flipped. So, let's consider the probabilities of these events:

Probability of exactly 5 flips out of 5 repetitions: p^5

Probability of exactly 4 flips out of 5 repetitions: 5*p^4(1−p)

Probability of exactly 3 flips out of 5 repetitions: 10*p^3(1−p)^2

So, the effective bit error rate (BER) is the sum of these probabilities:

BER= p^5+5*p^4(1−p)+ 10*(p^3*(1−p)^2)

The bit error rate for a QPSK system under AWGN is p, where 0<p<0.5. What is the
symbol error rate for this system ?
In a Quadrature Phase Shift Keying (QPSK) system, each symbol carries 2 bits of information, and the
symbol error rate (SER) depends on the bit error rate (BER).
For QPSK modulation, there are four symbols: 2+j2,−2−j2,2+j2,2−j2}, each corresponding to a
different combination of two bits.
The symbol error rate (SER) can be calculated from the bit error rate (BER) using the relationship
between them. In QPSK modulation, each symbol is affected by two bits, so the SER is related to the
BER by:
SER=1−(1−BER)^2
Given that the bit error rate (BER) is p, we can substitute this value into the formula to find the
symbol error rate (SER):
SER=1−(1−p)^2

Assume that the transmit pulse t(u(t)−u(t−1)) is used for signaling in a AWGN channel.
Write the equation for the matched filter for this pulse? Here u(t) represents the unit
step signal.

8.Define symbol errors and bit errors in digital communications. Explain how they differ and their
impact on system performance.
Answer:
Symbol Errors: Symbol errors occur when the received symbol is different from the transmitted
symbol. This can happen due to noise, interference, or other impairments in the communication
channel.
Bit Errors: Bit errors occur when the received bit does not match the transmitted bit. A symbol error
can result in multiple bit errors depending on the modulation scheme used (e.g., QPSK, 16-QAM).
Symbol errors impact the correctness of the decoded symbols directly, whereas bit errors affect the
accuracy of the decoded bits, influencing the overall data integrity and quality of the communication
link
1) Explain the Gram-Schmidt orthogonalization process and its significance in linear algebra?
i.Definition: Gram-Schmidt orthogonalization is a method used to transform a set of linearly
independent vectors into an orthogonal or orthonormal set.
ii.Process:
*Start with a set of linearly independent vectors { V1,V2,…..,Vn}
*Keep the first vector, V1, unchanged.
*For each subsequent vector Vi, subtract its projection onto each previously orthogonalized vector
and normalize the result.
iii.Significance:
Facilitates easier computation and analysis by simplifying vector spaces.
Essential in solving problems involving least squares approximation, eigenvalue problems, and linear
transformations.
Provides a basis for constructing orthonormal bases for Hilbert spaces.

Explain the concept of Orthogonal Frequency Division Multiplexing (OFDM) in digital

communications. What advantages does OFDM offer over traditional modulation schemes?
Answer:
OFDM is a multi-carrier modulation technique where a high-data-rate signal is divided into multiple
lower-rate subcarriers that are orthogonal to each other.
Each subcarrier is modulated using a relatively low symbol rate, which helps combat frequency-
selective fading and improves spectral efficiency.
OFDM is robust against frequency-selective fading and can handle narrowband interference
effectively.
It supports adaptive modulation and coding, making it suitable for dynamic channel conditions.
OFDM is widely used in wireless communication systems such as Wi-Fi, LTE, and digital broadcasting
due to its resilience to multipath propagation and efficient spectrum utilization.

Explain the concept of error detection and correction codes in communication systems. Provide
examples of commonly used error control codes and discuss their properties
Error detection and correction codes are essential components of communication systems to ensure
reliable transmission of data over noisy channels. These codes add redundancy to the transmitted
data, which enables the receiver to detect and possibly correct errors that occur during
transmission.
One commonly used error control code is the Hamming code, which is a type of forward error
correction code. The (7,4) binary Hamming code, for example, encodes 4 bits of data into a 7-bit
codeword, allowing for the detection and correction of single-bit errors.

Properties of the Hamming code include:

It can detect and correct single-bit errors.
It has a minimum Hamming distance of 3, meaning any two codewords differ in at least three bit
positions, allowing for single-bit error correction.
It can also detect some double-bit errors, but cannot correct them.

Another example is the binary repetition code, where each bit of the data is repeated multiple
times. For instance, the (5,1) repetition code repeats each bit five times. While simple and capable
of detecting errors, repetition codes are inefficient in terms of bandwidth utilization.
Single parity check codes, such as the (3,2) binary single parity code, add an additional parity bit to
the data to ensure even parity. They can detect single-bit errors but cannot correct them.

In communication systems, how do we convert a signal from a passband format to a baseband

format?
Answer:
Converting a signal from passband to baseband involves a process called demodulation. It's the
counterpart of modulation, which is used to shift a baseband signal to a higher frequency for
transmission.
Here's how demodulation works:

The incoming passband signal, which has its information piggybacked on a high-frequency carrier, is
multiplied with a replica of the original carrier signal used for modulation. This process is often done
using a mixer circuit.
Ideally, the multiplication mixes the frequencies of the carrier and the signal, resulting in a
cancellation of the carrier frequency.
Depending on the modulation scheme used (amplitude modulation, frequency modulation, etc.),
the demodulation process extracts the original baseband signal, containing the information, at the
output.

Explain the role and functioning of a Phase-Locked Loop (PLL) in communication systems. Discuss
its components, operation, and applications, emphasizing its importance in maintaining signal
synchronization
Answer:
A Phase-Locked Loop (PLL) is a control system used in communication systems for various purposes,
including frequency and phase synchronization, demodulation, and clock recovery. It consists of
several key components,
including a phase detector, loop filter, voltage-controlled oscillator (VCO), and feedback loop.
Phase Detector: The phase detector compares the phase of the incoming signal (reference signal)
with the phase of the local oscillator output. It generates an error signal proportional to the phase
difference between the two signals.
Loop Filter: The loop filter filters the error signal from the phase detector to remove noise and
unwanted frequency components. It also shapes the loop response and determines the PLL's
stability and bandwidth.
Voltage-Controlled Oscillator (VCO): The VCO generates an output signal whose frequency is
controlled by an input voltage. The frequency of the VCO output is adjusted based on the filtered
error signal from the loop filter.
Feedback Loop: The output of the VCO is fed back to the phase detector, closing the loop. The
feedback loop continuously adjusts the VCO frequency to minimize the phase difference between
the reference signal and the VCO output.
Operation:
Initially, the PLL is unlocked, and the VCO output frequency may differ from the reference
frequency. As the phase detector detects a phase difference, it generates an error signal that is
filtered by the loop filter. The filtered signal adjusts the VCO frequency, reducing the phase
difference until it locks onto the reference signal.
Applications:
Frequency Synthesis: PLLs are used to generate stable and accurate output frequencies by
multiplying or dividing the reference frequency.
Clock Recovery: PLLs recover the clock signal from data streams in digital communication systems,
ensuring accurate timing synchronization.

1) Explain usage of Histograms in GNU Radio

Histograms in GNU Radio are visual representations of the distribution of signalvalues within a
specified range. They are useful for analyzing the characteristicsof signals and understanding their
statistical properties.
Source Selection: Choose a suitable source block within GNU Radio to generate the signal data for
analysis.
Variable Configuration: Declare and configure variables to defineparameters such as the number of
bins, range of values, and update rate for the histogram display.
Histogram Sink Block: Utilize the Histogram Sink block available in GNU Radio, which collects data
from the source block and generates thehistogram based on specified parameters.
Connect Blocks: Connect the output of the source block to the input of the Histogram Sink block to
feed signal data into the histogram analysis.
Visualization: Run the GNU Radio flowgraph to display the histogram either within the GNU Radio
Companion GUI or in a separate window, depending on configuration.

Explain 7,4 hamming code in GNU Radio.

In GNU Radio, the 7,4 Hamming code refers to a specific type of error- correcting code used for
transmitting and receiving digital data. This code is characterized by encoding blocks of 4 data bits
into longer codewords of 7 bits,providing the capability to detect and correct single-bit errors. Here's
an explanation of the 7,4 Hamming code in GNU Radio:
Encoding: The 7,4 Hamming code in GNU Radio encodes 4 data bits into longer codewords of 7 bits
using a specific encoding algorithm based on parity bits. These parity bits are calculated to ensure
that the overall codeword satisfies certain parity conditions, allowing for error detectionand
correction.
Parity Check Matrix: The 7,4 Hamming code is defined by a parity checkmatrix, which specifies the
linear transformation used to encode the input data bits into the codeword bits. This matrix defines
the relationships between the data bits and the parity bits, facilitating the encoding process.
Error Detection and Correction: The key advantage of the 7,4 Hamming code is its ability to detect
and correct single-bit errors in the transmitted data. By employing parity bits and specific parity
conditions,the receiver in GNU Radio can detect errors in the received codeword and correct them if
necessary, ensuring accurate data transmission.
Implementation in GNU Radio: GNU Radio provides blocks and modules for implementing the
encoding and decoding processes of the 7,4 Hamming code. These blocks enable users to encode
data into Hammingcodewords for transmission and decode received codewords to recover the
original data, effectively incorporating error correction capabilities into digital communication
systems.

Discuss some of the advantages of using the GNU Radio signal model forsoftware radio
development.

Open-source and free to use, fostering collaboration and customizationof radio functionalities.
Modular design with a wide variety of signal processing blocks that can beeasily integrated into
workflows.
Supports a broad range of hardware platforms, allowing developers tochoose the SDR or other
hardware that best suits their needs.
Python scripting capabilities enable rapid prototyping, automation oftasks, and easier development
compared to lower-level languages.
Large and active community providing support, tutorials, andcontributions to the
software.

1. Describe the process of constructing and visualizing constellations using GNU Radio.
 Solution
 Signal Generation: Use GNU Radio to create a flowgraph generating the
digital modulation signal.
 Symbol Mapping: Map digital bits to symbols in the modulation
constellation using the Map block.
 Adding Noise: Introduce noise using the Noise Source block to simulate
real-world channel conditions.
 Visualization: Utilize the Constellation Sink block to visually represent
the constellation diagram.
 Analysis: Analyze the constellation to evaluate modulation scheme
performance under different conditions.

How does a Parity Check Code work?

 The parity bit is calculated based on the number of 1s in the data block.
 If the number of 1s is even, the parity bit is set to 0, making the total number of 1s even (even
parity).
 If the number of 1s is odd, the parity bit is set to 1, making the total number of 1s odd (odd
parity).
 During transmission, the receiver recalculates the parity bit based on the received data and
compares it with the received parity bit to check for errors.

Discuss Costas loop and differential PSK in GNU Radio

The Costas loop is a type of carrier recovery mechanism used in digital communication systems,
particularly with phase shift keying (PSK) modulation schemes.
It operates by generating an error signal based on the phase difference between the received signal
and a local oscillator.
The Costas loop tracks the phase of the received signal by adjusting the phase of the local oscillator.
It continuously compares the phase of the received signal with the phase of the local oscillator and
adjusts the oscillator's phase to minimize the phase error.
Differential PSK is a variant of PSK modulation where the phase of each symbol is determined by the
phase difference between successive symbols.
GNU Radio provides blocks for both Costas loop carrier recovery and differential PSK modulation and
demodulation.
Costas loop provides robust carrier recovery, even in the presence of noise and frequency offsets,
ensuring accurate demodulation of PSK signals.

Explain how GNU Radio features can be extended using Python. Provide a detailed overview of the
process of integrating Python code with GNU Radio?
Process of Integrating Python Code with GNU Radio-
The process of integrating Python code with GNU Radio involves the following steps Importing GNU
Radio Python modules (gnuradio) and classes.
Creating custom Python functions or classes to implement desired functionality. Instantiating custom
blocks or algorithms within GNU Radio flowgraphs.
Connecting custom blocks with existing GNU Radio blocks to form complete signal processing chains.
Executing the GNU Radio flowgraph, which seamlessly integrates custom Python code with
built-in GNU Radio functionality.

Consider an OFDM system with the following parameters:

Total bandwidth B=20 MHz
Guard interval Tg=5 μs
Number of subcarriers N=64
Subcarrier spacing Δf=312.5 kHz
Calculate the symbol duration Ts in microseconds.
Determine the number of useful subcarriers excluding the DC subcarrier.
Calculate the data rate in Mbps for QAM modulation with 64-QAM constellation.
Determine the total number of subcarriers including the DC subcarrier.
Calculate the maximum achievable data rate (excluding the guard interval) in Mbps.

Symbol duration: Ts=1/Δf1 Ts=312.5×1031 Ts=3.2μs

Number of useful subcarriers: Nuseful=N−1 (excluding the DC subcarrier) Nuseful=64−1=63

Data rate for QAM modulation:

For 64-QAM, each symbol carries 6 bits (since log2(64)=6). Therefore, the data rate per
subcarrier is 6×(1/Ts1) bits per second. Convert to Mbps:
Data rate per subcarrier=6×(1/3.2×10^(-6) bps

Data rate per subcarrier=1.875Mbps Total data rate for all useful subcarriers:
Total data rate=Nuseful×Data rate per subcarrier Total data rate=63×1.875Total data rate=63×1.875
Mbps

Total number of subcarriers: Including the DC subcarrier: Ntotal=N (DC subcarrier + useful
subcarriers) Ntotal=64
Maximum achievable data rate (excluding the guard interval): Maximum data rate=Nuseful
×Data rate per subcarrier
Maximum data rate=63×1.875 Mbps

Consider a (7,4) Hamming code.

Calculate the number of parity bits.
Determine the positions of the parity bits.
If the original message bits are 1011, find the encoded message.
If during transmission, the received codeword is 1111010, determine the bit position that has an
error.
Correct the error and find the original message.

Number of parity bits: In a (7,4) Hamming code, there are 7 bits in total and 4 message bits.
Therefore, the number of parity bits is 7−4=3
Positions of the parity bits: The positions of the parity bits are powers of 2. So, parity bits are at
positions 1, 2, and 4.
Encoded message: Original message: 1011 Parity bit positions: P1, P2, P3 (positions 1, 2, 4) Calculate
the parity bits:
P1: XOR of bits in positions 1, 3, 5, 7 = 1 (odd parity)
P2: XOR of bits in positions 2, 3, 6, 7 = 1 (odd parity)
P3: XOR of bits in positions 4, 5, 6, 7 = 0 (even parity)
So, the encoded message is: 1111011
Error detection: Received codeword: 1111010 Calculate the parity bits: P1: XOR of bits in positions 1,
3, 5, 7 = 1 P2: XOR of bits in positions 2, 3, 6, 7 = 1 P3: XOR of bits in positions 4, 5, 6, 7 = 0 Check the
parity bits against the received codeword:
P1 (1st position) error,
P2 (2nd position) correct,
P3 (4th position) correct. So, the error occurred in the 1st bit position.
Error correction: Flip the bit at the error position (1st bit position) to correct the error. Corrected
codeword: 1111011 Extract the original message: 1011

ASSIGNMENT QUESTIONS

A QPSK constellation at the receiver seems to be rotating at 0.94 radians per second, and you
know that you are close to the correct frequency at the receiver. What is the frequency offset
QAM-16 constellation has 16 points, where the real and imaginary parts have amplitudes {-3, -1,
1, 3}. At the receiver, the effective amplitude gain of the channel is 0.5. What would be The
constellation amplitudes that would appear at the receiver in the absence of noise (without any
additional scaling)
A data baseband signal has a bandwidth of 20 kHz. What would be a suitable carrier frequency for
up-converting this data signal to pass-band?
sinc based ISI-free transmission over a channel requires a baseband bandwidth of 10 kHz. If we
use a root-raised cosine pulse with excess bandwidth of 25% to transmit at the same rate, the new
baseband bandwidth required is
Let X and Ybe i.i.d. random Gaussian variables with mean zero and unit variance. The variance
of X+Yis:
A binary signaling approach over a real AWGN channel uses the equiprobable
symbols −0.2−0.2 and 1.21.2. The boundary for optimal decisions at the receiver is:
A QAM-32 constellation can be used to send
A binary symmetric channel has a bit flip probability of 0.10.1. When 1000 bits are transmitted
through this channel, the most likely number of bit flips that occur is:
Consider the following data sequence fed to a histogram plotter: {6, 6, 2, 7, 0, 2, 2, 4,
2, 1, 4, 8, 4, 7, 6, 2, 2, 7}. The value on the x-axis corresponding to the highest y-axis
value in the histogram is:
X1,X2,…X10are i.i.d. real-valued random variables that are Gaussian with mean 0 and
unit variance. Let Y=2(X1+X2+…X10) The variance of Y is:

Fill in the blanks on the topic Understanding GNU Radio features for Digital Communication:Basic
blocks, input and output
In GNU Radio, basic blocks represent for signal processing and manipulation.
The block in GNU Radio is responsible for receiving signals fromexternal devices like software-
defined radios or files.
The block in GNU Radio is used for transmitting signals to external devices or saving them to files.
Basic blocks in GNU Radio can be connected in a _ to create complex signal processing
flowgraphs for digital communication.
Understanding the input and output blocks in GNU Radio is crucial for designing and implementing
communication systems.
Solution
building blocks
Input
Output flowgraph
digital
True or false
Signal processing methods play a negligible role in digital communication tasks.
Vectors are extensively used in digital communication for representing signals and data streams.
GNU Radio is solely designed for analog communication and lacks relevance in digital communication
systems.
GNU Radio provides tools exclusively for signal generation and doesn't support reception
functionalities.
Understanding GNU Radio is crucial for digital communication engineers as it facilitates prototyping
and implementing digital communication systems efficiently.
Solution
False True False False True

Fill in the blanks on the topic Pulse Shaping for ISI Free Signaling
Pulse shaping is a technique used in digital communication to mitigate caused by
overlapping symbols.
Pulse shaping helps in shaping the transmitted pulses to minimize betweenadjacent symbols.
One commonly used pulse shaping technique is the filter, which has the property of zero
intersymbol interference (ISI).
Raised cosine filtering reduces ISI by smoothly the edges of the transmittedsymbols.
Pulse shaping plays a crucial role in achieving high in digital communication systems by reducing
the impact of ISI on signal detection.
Solution
ISI (Inter-Symbol Interference)
Interference
Raised cosine
Tapering
Performance

Fill in the blanks questions on the topic of Gram-Schmidt Orthogonalisation

In the Gram-Schmidt orthogonalization process, the initial vector u1 is .
To compute the k-th orthogonal vector uk, we subtract the projection of vk onto previous vectors
1,2,…,u1,u2,…,uk−1, ensuring orthogonality through .
The normalization step in Gram-Schmidt orthogonalization ensures that the resulting vectors ek are
.
Gram-Schmidt orthogonalization is particularly useful in linear algebra for simplifying computations
involving .
The Gram-Schmidt orthogonalization process transforms a set of linearly independent vectors into an
set of vectors.
Solution
set equal to v1.
subtraction.
unit vectors.
orthogonal bases
.orthonormal.
Fill in the blanks on the topic of symbol error rate and bit error rate

The Symbol Error Rate (SER) is a measure of the of symbol errors in a digitalcommunication system.

The Bit Error Rate (BER) is a measure of the _ of bit errors in a digitalcommunication system.

The SER is typically used to evaluate the performance of modulationschemes.

The BER is often utilized to assess the performance of communicationsystems.

The SER is defined as the ratio of the number of symbol errors to the total number of

transmitted.

Solution
Probability

Probability

Digital

Binary

Symbols