Download GTU BE/B.Tech 2019 Winter 7th Sem New 2171708 Digital Signal Processing Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- VII (New) EXAMINATION — WINTER 2019

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Subject Code: 2171708 Date: 26/11/2019
Subject Name: Digital Signal Processing
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:

1. Attempt all questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) How Digital signal processing is better than Analog signal processing? Explain in brief. [03]

(b) A discrete time signal is given by
x(n)={2,1,1,2,1}

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sketch the following signal:
(1) x (n+1) 2)x(n-2)

(c) A Digital communication link carries binary coded words representing samples of an input signal
X a(t) =3 cos600p t + 2 cos1800p t
The link is operated at 10000 bits/sec and each input sample is quantized into 1024 different voltage level.

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(a) What is the sampling frequency & folding frequency?
(b) What is the Nyquist rate for the signal X a (t)?
(c) What are the frequencies in the resulting discrete time signal x (n)?
(d) What is the resolution ? [07]

Q.2 (a) Determine the autocorrelation of the sequence [03]

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x (n) ={1,5,1,2}

(b) Obtain the linear convolution of [04]
x (n) = {1,2,2,1} h(n) = {1,2,1}

(c) Determine the response of the system [07]
y (n) =5/6 y (n-1)-.1/6 y(n-2) + x(n) to the input signal

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X (n) = d(n)

OR

(c) Prove that LTI system is stable if its impulse response is absolutely summable. Test the stability of a system where impulse is [07]
h (n) = aⁿ u(n).

Q.3 (a) Prove that LTI system is causal if its impulse response [03]

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h(n)=0 for n<0

(b) Determine if the following discrete time systems are [04]
(1) Causal or non causal
(2) Linear or non linear
(a) y(n) = cos x(n)

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(b) y(n) =x(n²)

(c) Determine the inverse Z transform of the following using partial fraction expansion method. [07]
X(z) = 2z³ /(z-1)(z-1/2)² |z| > 1

Q.3 (a) Find the Z transform and sketch ROC of [03]
x (n)=aⁿu(n) + d (n-3)

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(b) State & prove differentiation property of Z transform. [04]

(c) Find the inverse Z transform of the following using long division method. [07]
(1) X(z)=z/z-1 |z|>1
(2) X(z)=z/ z-a if |z| <|a|

Q.4 (a) Describe the relationship between DFT & Z- transform. [03]

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(b) Explain linearity & periodicity properties of DFT. [04]

(c) The transfer function of a causal LTI system is [07]
H(z)=(1-z^-1)/(1+3/4z^-1)
(1) Find the impulse response of the system.
(2) Find the output of the system to the input

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x (n) =(1/3)ⁿu(n) + u (-n-1)
(3) Is the system stable?

OR

Q.4 (a) Compute the DFT of the following: [03]
(1) x (n) = d (n)

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(2) x (n) = d (n —n₀)

(b) Find the circular convolution of the following sequences: [04]
x (n) = {1,2,3,4} h(n) ={2,1,1,2}

(c) Consider the LTI system initially at rest, described by the difference equation, [07]
y (n) =1/4 y (n-2) + x(n)

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(1) determine h(n) of the system
(2) Determine direct form —II, parallel form & cascade form realization of this system.

Q.5 (a) Explain frequency Aliasing. [03]

(b) Write the properties of [04]
(a) hamming window

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(b) hanning window

(c) Explain bilinear transformation-method of designing IIR filter. [07]

OR

Q.5 (a) Find inverse DFT of X(K) ={1,2,3,4} [03]

(b) The transfer function of analog filter is [04]

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H(s) =3/ (s+2)(s+3) with Ts=0.1 sec
Design IIR filters using bilinear transformation.

(c) Explain Radix-2 decimation in frequency FFT algorithm. [07]

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