Rajalakshmi Engineering College, Thandalam Deviation ratio = maximum Δf/Maximum fm

Department of ECE 9. What is direct FM?

In direct FM, the frequency of the carrier wave is directly varied in accordance with the
EC19402-Communication Theory modulating signal.
Possible 2 Marks Q&A 10. What is indirect FM?
Unit II – Angle modulation In indirect FM, first narrowband FM will be generated. Then frequency multiplier is employed
to generate required wideband FM.
1. State Carson’s rule for FM bandwidth. 11. How Narrowband FM is converted to Wideband FM?
Carson’s rule for FM bandwidth is defined as the twice the sum of frequency deviation and Frequency multiplier is employed to convert narrowband FM into wideband FM
modulating signal frequency.
i.e Bandwidth = 2 (Δf+fm)
2. Define frequency modulation.
In frequency modulation, the frequency of the carrier wave is varied in accordance with the
modulating signal.
12. Draw the block diagram of a frequency multiplier.
3. A carrier of frequency 100 MHz is frequency modulated by a signal x(t) = 20 sin (200π*103t).
What is the bandwidth of FM signal if the frequency sensitivity of the modulator is 25
KHz/volt?
Soln: Frequency sensitivity Kf = 25K Hz/volt
Comparing x(t) = 20 sin (200π*103t) with x(t) = Vm sin (2πfmt)
Vm= 20 volts & fm=100 KHz
By Carson’s rule,
Bandwidth = 2 (Δf+fm) 13. Find the bandwidth required for an FM signal in which the modulating signal is 2 KHz
WKT, Δf = Kf Vm = 25*103 * 20 = 500 KHz and maximum frequency deviation is 14 KHz.
Bandwidth = 2(500*103+100*103) = 1200 KHz (or) 1.2 MHz. Soln:
4. Define phase modulation. Δf = 14 KHz and fm= 2 KHz
In phase modulation, the phase of the carrier wave is varied in accordance with the modulating Bandwidth = 2 (Δf+fm)
signal. Bandwidth = 2 (14*103+2*103) = 32 KHZ
5. Bring out the differences between NBFM & WBFM. 14. Mention the disadvantage of ratio detector.
The only the drawback of the ratio detector is, the output is half compared to the Foster-Seeley
Narrow Band FM Wide Band FM discriminator.
15. Mention the disadvantage of Foster-Seeley discriminator? Mention a method to overcome.
Modulation index is smaller than 1 i.e Modulation index is greater than 1 i.e β>1
The only disadvantage of a Foster-Seeley discriminator is it needs a separate amplitude limiting
β<1
circuit (i.e limiter circuit for noise removal). It can overcome by Ratio detector.
It consists of one carrier component It consists of one carrier component and
16. Bring out the differences between amplitude modulation and frequency modulation.
and two side bands infinite side bands
Bandwidth required is 2fm Bandwidth required is 2Nfm max S.No. Amplitude Modulation Frequency Modulation
1. The amplitude of the carrier wave will The frequency of the carrier
Frequency deviation is about 5 KHz Frequency deviation is 75 KHz be varied in accordance with the wave will be varied in
Used in mobile communication Used in radio broadcasting modulating signal accordance with the
6. Mention the methods of generating an FM wave. modulating signal.
(i) Direct FM or Direct method 2. Spectrum of AM consists of one carrier Spectrum of FM consists of
(ii) Indirect FM or Indirect method component and two side bands. one carrier component and
7. Draw a feedback scheme to achieve frequency stabilization of a frequency modulator. infinite number of side bands.
3. Requires less transmission bandwidth. Requires more transmission
bandwidth.
4. Noise interference is more (poor audio Noise interference is less
quality). (better audio quality).
5. It operates in MF & HF ranges. It operates in VHF & UHF
ranges.
6. Bandwidth = 2fm Bandwidth = 2(Δf+fm) or 2Nfm
max
Any four only
17. Point out the disadvantages of balanced slope detector.
Disadvantages of balanced slope detector are:
8. Define deviation ratio.
Deviation ratio is the ratio of maximum carrier frequency deviation to the maximum
modulating frequency.
 i. The linear characteristics is limited to a small frequency deviation (Δf)
ii. It is very difficult to align because of three different frequencies to which various tuned Rajalakshmi Engineering College, Thandalam
circuits are to be tuned. Department of ECE
iii. The tuned circuit output is not purely band limited and hence low pass RC filter of
envelope detector introduces distortion. EC19402-Communication Theory
18. Define modulation index for frequency modulation. Possible 2 Marks Q&A
The modulation index (β) of frequency modulation is defined as the ratio of maximum Unit III – Random Process
frequency deviation (Δf) to the modulating frequency (fm).
i.e β = Δf /fm 1. List out the condition for ergodic random process.
19. State the principle used in FM demodulation.
The principle used in FM demodulation: A random process is said to be an ergodic random process, it has to satisfy the following 2
i. Frequency modulated (FM) signal is first converted into its corresponding amplitude conditions:
modulated (AM) signal by using frequency discriminators. – 1 Mark (i) Ensemble mean = Time mean
ii. The original modulating signal is recovered from AM signal by using an envelope (ii) Ensemble autocorrelation = Time autocorrelation
detector.
20. What is PLL?
2. Define random process.
PLL is Phase Locked Loop. It consists of phase detector, low pass filter, amplifier and voltage
controlled oscillator (VCO). PLL is used to lock the output frequency and phase to the Random process is an ensemble or sample space which consists of all the sample points
frequency and phase of the input signal.
whose outcome is a random function of time.
************************ 3. Define auto correlation.
The auto correlation provides a measure of similarity or coherency between a given signal
and the replica of the same signal delayed by a particular time period.

i.e Rx(t1,t2)=E[X(t1)X(t2)]

4. State Gaussian process.

Suppose we weight the random process X(t) by some function g(t) and then integrate the product
g(t) X(t) over the observation interval 0 to T, there by obtaining a random variable Y. If the
weighting function g(t) is chosen such that the mean square value of the random variable Y is finite
and if the random variable Y is a Gaussian random variable for every g(t), then the random process
X(t) is said to be Gaussian process.

5. Define a random variable.

A random variable may be defined as a function that maps every outcome in a sample space
to a real number.

6. The pdf of a random variable is given as fX(x) =k for a≤x≤b and 0 otherwise where k is
a constant. Find the value of k.
Soln:
∞
fX(x) dx=1
-∞
b
K dx=1
a

K=1/(b-a)
7. When a random process is said to be ergodic random process? 15. Write the difference between random variable and random process.
A random process is said to be an ergodic random process, it has to satisfy the following 2
conditions: Random variable Random process
(i) Ensemble mean = Time mean
(ii) Ensemble autocorrelation = Time autocorrelation It is a function that maps every It is an ensemble or sample space which
outcome in a sample space to a real consist of all the sample points whose
8. Mention any two properties of autocorrelation function. number. outcome is a random function of time.
i) Symmetry Rx()= Rx(-)
ii) The maximum value of auto correlation function occur at =0 Only ensemble average can be calculated. Both ensemble average and time average can
be calculated
9. List down the conditions for wide sense stationary process. It need not be the function of time It is a function of time
A random process is said to be wide sense stationary random process the following two
conditions to be satisfied: Random variables are not further classified Random process can be stationary are ergodic.
i). Mean E[X(t)]= Constant
ii) Autocorrelation depends only on time difference  (i.e should be independent of actual time
instant).
16. Bring out the differences between autocorrelation and cross correlation.
10. Define power spectral density.
Autocorrelation Cross correlation
The power spectral density (PSD) of the signal describes the power present in the signal as a It provides a measure of the similarity The cross correlation two random process
function of frequency. The PSD of a random process X(t) is given by the Fourier transform (FT) between a given signal and the replica of is defined as a measure of the similarity
of its autocorrelation function the same signal delayed by a particular between a signal and a time delayed
time. version of a second signal.
The maximum value of the autocorrelation It does not have maximum value at origin.
functionoccurs at origin.
The autocorrelation is given by RX() = The cross correlation is given by RX(t1,t2) =
E[X(t1) X(t2)] E[X(t1) Y(t2)]

11. When a random process is called deterministic?

A random process whose future values can be exactly predicted from the knowledge of all 17. State Wiener-Khintchine theorem.
past values is said to be deterministic random process.
The auto correlation of power signal and its power spectral density form a Fourier transforms
pair. This relation is called Wiener-Khintchine theorem.
12. When a random process is said to be stationary random process?
A random process X(t) is said to be stationary random process, if all the statistical properties of
the random process are not affected by shift in time. This means that random process X(t) and
X(t+) possesses the same statistical properties for any value of T.

13. Define white noise. Write its PSD.

White noise is a random signal having equal intensity at different frequencies, giving it a
constant power spectral density. Its PSD is N0/2. 18. Mention the types of random variables.
14. What is cross correlation? Types of random variables are:
The cross correlation two random process is defined as a measure of the similarity between a
signal and a time delayed version of a second signal. i. Discrete random variable

ii. Continuous random variable.

19. Mention the types of random process.

Types of random process are:

i. Stationary and non-stationary random process

ii. Discrete and continuous random process

iii. Deterministic and non-deterministic random process

iv. Wide sense stationary random process

v. Strict sense stationary random process

vi. Ergodic random process.

20. Write down the properties of Gaussian process.

21. When a random process is called strict sense stationary?

A random process X(t) is said to be strict sense stationary, if all the statistical properties of the
random process are not affected by shift in time. This means that random process x(t) and x(t+T)
possesses the same statistical properties for any value of T.

22. Define weak sense stationary or wide sense stationary (WSS) random process.
A random process is said to be weak sense stationary or wide sense stationary random
process the following two conditions to be satisfied:
i). Mean E[X(t)]= Constant

ii) Autocorrelation depends only on time difference (i.e should be independent of actual time
instant).

23. Mention any two properties of power spectral density.

The two properties of power spectral density are:

i. The power spectral density non-negative i.e SX(f)≥0

ii. The power spectral density of a real valued random process is an even function of frequency
i.e SX(-f) = SX(f)