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QUESTION: 1

The DSB-SC signal recevied at the output of a channel is given as S(t) = 2 cos2π(10^{3} - 0.5). cos2π(10^{6} -

1). Determine the group delay and phase delay introduced by the channel.

Solution:

For an amplitude modulated signal

the delay in carrier frequency

component gives phase delay and

delay in baseband (message)

signal gives the group delay.

{Reference: Page No 98, Simon

Haykin, common system 3rd

edition}

QUESTION: 2

Which of the following is incorrect about hilbert-transform?

Solution:

x_{h} (t) is delayed version by -90^{0} of

x(t)

QUESTION: 3

An amplitude modulated signal is given as s(t) = 14 cos8000πt + 20 cos10000πt + 14 cos12000πt.

Determine the modulation depth.

Solution:

QUESTION: 4

An amplitude modulated signal is given as S(t) = 10 (2 + cos2π x 10^{4}t) cos2π x 10^{7}t. If the carrier

frequency component is suppresed before transmission, then determine the percentage power

saved.

Solution:

QUESTION: 5

Suppose that non linear device (NLD) is available for which the output voltage V_{0} and input voltage V_{i} are related by V0(t) = a1 where a_{1} and a_{3} are constants. Let V_{i} = m (t) + cos2πf_{c}t and a_{1} = 1, a_{2} = 1. To generate a DSB-SC signal having carrier frequency is 5MHz, this NLD is followed by a BPF of appropriate centre frequency and band width. Determine f_{c}

Solution:

QUESTION: 6

Consider a square law device having input voltage V_{i} and output voltage V_{0} are related as

This SLD is used to generate an standard AM with a carrier frequency of 3MHz, as shown in the circuit below.

Determine the maximum bandwidth of message signal m(t) so that spectrum of s(t) is nonoverlapping.

Solution:

i.e the maximum bandwidth of

message signal may be 1MHz

QUESTION: 7

A message signal m(t) = 4 cos2πx 10^{4} t is used to generate an FM signal. Determine the minimum

value of (Δf)_{max} so that modulation efficiency is 100%.

Solution:

M(t) = 4cos2π x 10^{4}t

Here Am = 4, fm = 10 KHz,

Modulation efficiency is 100%

when β_{f} = 2.4, 5.5, 8.6-----

QUESTION: 8

A phase-modulated signal is given as S(t) = 30 cos[2πx10^{8}t + 100 cos2πx10^{4}t]. Determine the

transmission bandwidth required according to carson’s approximation.

Solution:

= 2 (100 + 1) x 10

= 20 x 101

= 2020 KHz

= 2.02 MHz

QUESTION: 9

Consider an FM signal, S(t) = 10 cos[2π x10^{7}t + 10 sin2π x10^{3}t]. Determine Kp/Kf if the above modulated signal is assumed phase-modulated signal.

Solution:

QUESTION: 10

The following message signal m(t) is given to both frequency modulator and phase modulator. If

the maximum phase deviation of both FM and PM is same, determine the Kf/Kp.

Solution:

and maximum phase-deviation of

FM signal

QUESTION: 11

Consider a sine wave of frequency 2 KHz and peak amplitude AM. This signal is applied to a delta modulator of step-size 0.4 Volt and sampling period 3.18 x 10^{-6} sec. What is the maximum power that

may be transmitted without slopeoverload distortion?

Solution:

QUESTION: 12

A PCM system uses an uniform quantizer followed by a 7-bit binary encoder. The bit rate of the system is equal to 50x10^{6} bits/ second. Determine the output signal to quantization noise ratio when a full-load sinusoidal modulating signal of frequency 1MHz is applied to the input.

Solution:

(SNR) = (6n + 1.8) dB

= 6 x 7 + 1.8

= 43.5 dB

QUESTION: 13

An analog signal is sampled, quantized and encoded into a binary PCM system. The specifications of the PCM system include the following: Sampling role = 8 KHz Number of representation levels = 64

Determine the minimum bandwidth required if PCM wave is transmitted over a baseband channel.

Solution:

QUESTION: 14

A binary PCM system uses pulse P(t) to transmit symbol 1 and - P(t) to transmit symbol 0. The additive noise at the reciever input is white and Gaussian, with zero mean and power spectral density

10^{-10} W/Hz. Assuming that symbols 1 and 0 occur with equal probability, determine the probability of error at the reciever output.

Solution:

For binary polar signal the

probability of error is given as

QUESTION: 15

A source emits one of four symbols S_{0}, S_{1}, S_{2} and S_{3} with probabilities 1/3, 1/6, 1/4 and 1/4 respectively.

The successive symbols emitted by the source are statistically independent. Calculate the entropy

of the source.

Solution:

QUESTION: 16

Consider a sinusoidal signal with random phase, defined by X(t) = where A and f_{c }are constants and θ is a random variable that is uniformly distributed over the interval Determine the autocorelation function of X (t)

Solution:

The probability function of random

variable is given as,

Now the auto-corelation function

of X(t)

QUESTION: 17

The probability density function of a random variable is shown in the figure. Determine P (X 0)

Solution:

The probability for X0 is exactly

1. (i.e whole area under density

function curve)

QUESTION: 18

A 1W video signal having bandwidth of 200 MHz is transmitted to a reciver through a cable that has 50 dB loss. If the efficitive two sided noise power spectred density at the receiver is 10^{-20} Watt/Hz, then the signal to noise ratio at the receiver is

Solution:

P_{S} = 1 W

Since cable loss is 50 dB (105), So

power at the input of reciever

P_{S} = 10^{-5} Watts

Noise power = 2 x200 x10^{6} x10^{-20}

2, Because of two sided PSD

= 4 x 10^{-12} Watts

Therefore

QUESTION: 19

A computer puts out binary data at the rate of 56 kbps. The computer output is transmitted using a

baseband binary PAM system that is designed to have a raised cosine spectrum. Determine band width

required if the roll-off factor is 0.5.

Solution:

Bit Rate (R_{b}) = 56 Kbps

Since it is transmitted by 2-array,

so minimum bandwidth without

raised-cosine pattern

and minimum bandwidth with

raised-cosine pattern

QUESTION: 20

A QPSK system transmits binary data at the rate of 2.5 x 10^{6} bit per second. Determine minimum

bandwidth required for the transmission.

Solution:

QUESTION: 21

For attenuation of high frequencies we should use

Solution:

Since X_{c} for high frequencies is low, the high frequencies are shunted to ground and are not transmitted.

QUESTION: 22

The pulse shown in the figure, is given as the input of a matched filter. Determine the peak value of

the output of matched filter.

Solution:

QUESTION: 23

A binary random variable X takes the value of 1 with probability 2/3. X is input to a binary symetric

channel with cross-over probability 1/2.

Determine the value of H(Y)

Solution:

QUESTION: 24

A voice-grade channel of the telephone network has a bandwidth of 3.4 KHz calculate the information capacity of the telephone channel for a signal to noise ratio of 30 dB.

Solution:

Capacity of a gaussian channel is

given as,

C = BW log_{2} (1 + SNR)

Here SNR = 30 dB (1000)

So,

QUESTION: 25

Determine the minimum sampling frequency of x(2t), where x(t) = sine (1000t)

Solution:

Minimum sampling frequency of

x(t) is 1000 Hz (1KHz)

So, minimum sampling frequency

of x(2t) is 2KHz

QUESTION: 26

The probability density function of random variable X is given as

Determine the variance (σ^{2}) of random variable X.

Solution:

Given

Comparing this equation with the

standard gaussian probability

density function

i.e

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