Download GTU BE/B.Tech 2018 Winter 7th Sem New 2170914 Digital Signal Processing Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VII (NEW) EXAMINATION - WINTER 2018
Subject Code: 2170914 Date: 15/11/2018
Subject Name: Digital Signal Processing
Time: 10:30 AM TO 01:00 PM Total Marks: 70

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Instructions:

1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

MARKS

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Q.1 (a) A discrete —time signal x(n) is given below :
X(n) = {1,2,1,-2,1,2,3,4,14} 03
Sketch and label carefully each of the following signals:
(1) x(n-2) (i) x(-4-n) (iii) x(n/2)

(b) List advantages of Digital Signal Processing over Analog Signal Processing. 04

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(c) Find the linear convolution of following pairs of discrete sequences 07
(1) x1(n)={1,2,3,4,12,4,6} h1(n)= {4,3,2,1}
(1) x2(n) = {1,2,1,2,1,2,1} h2(n)= {1,2,3,4,3,2,1}

Q.2 (a) Obtain Fourier transform of single sided exponential pulse 03
x(n) = aⁿ u(n)

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(b) Check the following systems for time invariance and Linearity : (i) y(n) =n[x(n)]^* (i) y(n)= a[x(n)]^*+b x(n) 04

(c) Calculate DTFT of following signals 07
(i) x(n)=[1/4,1/2, 1/4] (i) x(n)=2(1/2)ⁿ u(n)

OR

(c) Explain Inverse system, minimum phase system and all pass system. Determine Inverse of the system characterized by y(n)=0.5y(n-1)+x(n).assuming zero initial conditions. 07

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Q.3 (a) Find the Z Transform of (1/3)ⁿ u(n-1) 03

(b) The impulse response of the LTI system is h(n)={2,4,5,6}. 04
Determine the response of the system to the input signal x(n)={1,1,2,3}

(c) Determine the inverse z-transform of the function 07
X(z)= z/(1-1.5z^-1+0.5z^-2) , |z|>1

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OR

Q.3 (a) Find Z-transform of x(n) = [2(4)ⁿ — 4(2)ⁿ ] u(n) 03

(b) State and prove the differentiation property of Z transform. 04

(c) Determine the response of the system, 07
y(n) = 5/6 y(n—l) - 1/6 y(n-2) + x(n) to the input signals. x(n) = δ(n)- 1/4 δ(n-1)

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Q.4 (a) Define DFT. 03

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(b) Define and explain properties of IDFT. 04

(c) Explain 8-point DFT from two 4 point DFTs using radix-2 Decimation in frequency (DIF) FFT algorithm. 07

OR

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Q.4 (a) Find the Circular convolution of following pairs of discrete sequences 03
(1) X1(n) = {3,2,3,4} X2(n) :{ 1,3,2,2,1}

(b) Obtain the value of X(4) for 8 point DFT if x(n) = {1,-1,0,2,1,-2,-1,1} 04

(c) Derive DIT FFT flow graph for N = 4 hence find DFT of x(n) = {1,2,3,4} 07

Q.5 (a) Write a note on windowing. 03

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(b) Determine H(Z) by using impulse invariant method if H(s) = 1/s and sampling time is 0.01 sec. 04

(c) Obtain Direct Form I & II realization of a system described by y(n) —1/6 y(n— 1) + 1/3 y(n-2) = x(n) + 2x(n-2) 07

OR

Q.5 (a) Compare Decimation in Time and Decimation in Frequency. 03

(b) Explain Floating point Digital signal processors. 04

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(c) With the help of a neat sketch, explain Digital Signal Processor architecture. 07

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