SET – I

01. Which of the following represents the phase response of a distortionless transmission system?

02. The PSD of a signal x(t) is 8(). Then x(t) is given by (a) 0.5 (b) 0.5(c) sint (d) 2

03. The pdf of random variable X is given by

fx(x)= ax2 ; -b < x <b 0 ; otherwise

The relation between a & b is ____

(a) b =

(b) b =

(c) b =

(d) b =

04. A signal m(t) = cos200t+2cos320t is ideally sampled at fs = 300Hz. If the sampled signal is passed through an ideal low pass filter with a cutoff frequency of 250Hz . What frequencies (in Hz) will appear at the output?(a) 100,120,140,160(b) 100,140,180,200(c) 100,140,160,200(d) 100,140,160,180

05. A delta modulator is designed to operate on speech signals limited to 2.8kHz. The sampling rate is 10 times the Nyquist rate. Step size is 120 mV.The modulator is tested with a sinusoidal signal of 1.2kHz. The maximum amplitude of the test signal to avoid slope overload distortion is(a) 0.891V (b) 8.91V(c) 0.0891V (d) 1.0891V

06. An analog signal is band limited to 4.5kHz.The signal is sampled at 2 times the Nyquist rate and each sample is quantized into 1 of 128 levels which are equally likely. The SNR is 15 dB. The minimum bandwidth of the channel required for error free transmission is (a) 20kHz (b) 22 kHz(c) 25.06kHz (d) 25.06MHz

07. If FX(x) in the given figure is the

cumulative distributive function (CDF) of random variable X then what will be its probability density function(PDF) fX(x) ?

()(a)

()

(b)

()(c)

()(d)

x

FX(x)

(d) The figure is not valid cumulative distributive function (CDF).

08. In a binary communication channel shown below

m0,m1 denote the event of transmitting 0&1 respectively and due to channel noise 0 can be received as 1 and vice versa. All the related probabilities are shown in the channel . If 1 was received what is the probability that 1 was transmitted ?(a) 0.887 (b) 0.707(c) 0.778 (d) 0.07

09. Assume fX(x) = Aexp(–P )+ Bexp(– )

where P = 1 and Q = 1/4 . fx(x) is the pdf for the real random variable X over the entire x-axis. A & B are both positive numbers the equation relating A & B is(a) A+4B = 2 (b) 4A+B = 2

(c) 2A+B = 1(d) A+2B = 1

10. The joint probability density function of two random variables is fXY(x,y) = k[x2+y] ; k = 3/44, x (2,3) , y (0,2)then E(x) is (a) 88/225 (b) 225/88(c) 85/229 (d) 229/85

11. The input to a matched filter is given by s(t) = 7 cos(2×105t); 0<t<10-3sec

0 otherwiseThe peak amplitude of the filter output in ‘mV’ is______

12. Consider the equations /statements given below

1. Jn() =

2. J–n() = (–1)n Jn ()

3.

4. Q(z) =

5. Q(0) =

6.Q(–z) = 1– Q(z) ; Z 0Which of the above equations/statement is true?(a) 1, 2, 5, 6 (b) 1, 4, 5, 6(c) 1,2,3,4,5 (d) 1,2,3,4,5,6

13.

The above fig shown is a 4 :1 multiplexer which has selection lines as X & Y. X & Y are discrete RV’s taking binary values 0 & 1. The probability of occurrences of a various symbols are given as P[X = 0, Y = 0] = 0.35

x

(a) fX(x)

x

(b)

fX(x)

x

(c) fX(x)

m0

m1

r0

r1

P(m0) =0.5

P(m1) =0.5

0.2

0.8

0.33

0.7

X Y

Fm0

m1

m2

m3

I0

I1

I2

I3

4:1 MUX

3/4 1 2 3 41/2(a)

P [X = 0, Y =1] = 0.15P [X = 1, Y =0] = 0.30P [X =1, Y =1] = 0.20The symbol rate is 1000 symbols /secThe average information rate at the output of the mux in (bps) is (a) 2691 (b) 9216(c) 1926 (d) 6291

Each Question Carries Two Marks20 2 = 40

14. A bipolar signal si(t) is a +1V or –1Vpulse during the internal (0,T). Additive White Gaussian noise with power spectral density /2 = 10–5 W/Hz is added to the signal. The maximum bit rate that can be sent with a bit error probability of pe 10–4,Given thatQ(x) = 10-4 for x = 3.71 is(a) 7.62 kbps (b) 7.26 kbps(c) 2.76 kbps (d) 7.26 Mbps

15. The matched filter output over (0,T) to the pulse waveforms(t) = is(a) e–Tcosht (b) e–Tsinht

(c) (d)

16. Let m(t) be a periodic triangular wave with 10–3 sec with m(t)max = –m(t)min = 1 V. The max. & min. values of the instantaneous frequency for a phase modulated wave with kp

= 2 rad/sec.(a) 98 kHz & 102 kHz(b) 99 kHz & 101 kHz(c) 92 kHz & 108 kHz(d) 96 kHz & 104 kHz

17. Consider a random variable Z such that Z = pX+qY, where p &q are arbitrary constant. If X & Y are independent random variable, then which of the following is true?(a)

(b)

(c)

(d)

18. Consider a message signal m(t) = 4cos200t+6cos400tIf this signal under goes FM modulation with kf =8 Hz/V then the BW of the modulated signal is

(a) Hz (b) Hz

(c) Hz (d) Hz

19. Two random variable X & Y with pdf shown in figure below are added to form another random variable Z.Z = X +Y

Given that X & Y are independent random variables is, the pdf of Z is 20. An information source can be modeled as a

band limited process with a bandwidth of 6000 Hz. This process is damped at a rate higher than the Nyquist rate to provide a guard band of 2000 Hz. It is observed that the resulting samples takes values in the set A = {–4, –3,–1,2,4,7} with probabilities 0.2, 0.1, 0.15, 0.05, 0.3, 0.2. The entropy of the discrete time source in bits/sec is

(a) 33750 bps (b) 33722 bps(c) 33900 bps (d) 34000 bps

21. Consider the 2, 8 point QAM signal constellations shown in figure given below. The minimum distance between adjacent points is 2A. The average transmitted powers for constellation A & B (assuming that the signal points are equally probable) respectively are ________ & __________

3/4

1 2 4 5

1/2

(b)

1/12

3 5 7 9

(c)

1/4

3 5 7 9

(d)

A

2 4

Pdf of X

B

1 5

Pdf of Y

Fig A: Constellation A Fig B: Constellation B

(a) 6A2, 6A2 (b)

(c) (d) 6A2, 9A2

22. The system shown in figure is used to generate an AM signal. The modulating signal m(t) has zero mean & its maximum (absolute) value is AM = max . The NL device has a i/p – o/p characteristics y(t) = a x(t) + b x2(t). The BPF has centre frequency fo

If modulation index of the AM signal at the output is 0.8, a = 15, m(t) = 3cos , the value of b is ____ .

23. What is the resulting SQNR (in dB equivalent to the nearest integer) for a signal uniformly distributed in [–1,1], when uniform PCM with 256 quantization levels is used ?

24. A stationary source is distributed according a

triangular PDF, fX(x) = . This source

is quantized using a 4-level uniform quantizer described below

The entropy of the quantized source is _______

(a) 1.56 bits/symbol (b) 1.8311 bits/symbol(c) 2.12 bits/symbol (d) 2.42 bits/symbol

25. A binary communication system transmits signals si(t) (i=1,2). The receiver test statistic z(T) is z(T) = ai + no

Where a1 = +1 and a2 = –1 and no is uniformly distributed, yielding the conditional density functions f(z|si) given by

The probability of error Pe for the case of equally likely signals, using an optimum decision threshold is

26. Joint density function of 2nRV’s is

for x(2, ) and y(0, 1).

Then the value E(y) is (a) 9/10 (b) 9/15(c) 9/20 (d) 9/16

27. Two constellation diagrams of 6 QAM are shown below (All symbols are equiprobable)

Distance between any two nearest constellation point is ‘d’. Constellation (II) is generated from constellation (I) by shifting left as well as shifting downward by distance of d/2. The ratio of average energy of constellation (I) to constellation (II) is _______

28. Consider a message signal m(t) =e–tu(t). The maximum frequency present in this signal is decided up to the point at which magnitude becomes one fifth of the maximum value.If single side band suppressed carrier is used as a modulation scheme with carrier frequency 200MHz, then bandwidth of the modulated signal (in Hz) is

(a) (b)

m(t) x(t) y(t) p(t)

AM signalBPF

Non linearmemorylesssystem

Cos

(I) (II)

(c) (d)

29. Which of the following can be a suitable autocorrelation function?1. Atri(/0) ; where tri(x) is unit triangular

function2. Asin(0)3. Acos(0)4. A rect (/0)

(a) 1 only (b) 1,3(c) 1,3,4 (d) 1,2,3,4