GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- V EXAMINATION - SUMMER 2020
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Subject Code: 2150307 Date:29/10/2020Subject Name: Digital Signal Processing
Time: 02:30 PM TO 05:00 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.
MARKS
Q.1 (a) Define following signals with proper example: 03
1. Digital Signal
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2. Continuous Time Signal3. Power Signal
(b) Draw the following signals, if 04
x(n)=1{1,2,3,4,5,6}
1. x(-n)
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2. x(-n-1)3. x(n/2)
4. 2x(n)
(c) List out different properties of Z-Transform. Explain any three in detail. 07
Q.2 (a) Sketch the following Signals. 03
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1. d(n-3)2. 3(n+3)
3. d(-n)
4. 3(-n+2)
(b) Check y(n)=nx(n-1) is 04
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1. Static or Dynamic2. Time variant or Time In-variant
3. Linear or Non Linear
4. Causal or Anti Causal
(c) For the system 07
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Y (n)-3/4y (n-1) +1/8y (n-2) =x (n) +1/2x (n-1). Derive the direct form I and direct form II structures.OR
(c) Draw the parallel form realization of following signal 07
y(n) =5y(n—1) —2y(n —2) + x(n) + 4x(n —1).
Q.3 (a) What do you mean by correlation? Explain with examples. 03
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(b) Find out convolution of following sequences 04
x(n)= dn u(n) and h(n)=u(n-5).
(c) Consider a sequence x[n]={1,1,-1,-1,-1,1,1,-1} determine the DFT X[k] of x[n] using the decimation-in-time FFT algorithm. 07
OR
Q.3 (a) Obtain the inverse z-transform of the following: 03
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X(z)=log(1 +az-1), |z|>|a|(b) Find out the Z-transform of following: X(n) = anu(n) 04
(c) Given x(n)={1,2,3,4,4,3,2,1}, find X(k) using Decimation-In-Frequency FFT algorithm. 07
Q.4 (a) Explain Mapping between S-plane and Z-plane. 03
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(b) Explain Goertzel algorithm to compute DFT. 04
(c) Obtain the lattice filter implementation for the all-pole filter 07
H(z)= 1/(1-0.2z-1 +0.4z-2+0.6z-3)
OR
Q.4 (a) What is Equiripple Approximation? 03
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(b) What is aliasing? Explain various methods to eliminate aliasing effect. 04
(c) Find out 8-point DFT of x(n)={1,2,1,2} using Radix -2 DIF-FFT algorithm. 07
Q.5 (a) List the advantages of digital filter. 03
(b) Compare Butterworth and Chebyshev filters. 04
(c) Explain IIR filter design by bilinear transformation method. 07
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OR
Q.5 (a) What is “twiddle factor” of DFT? 03
(b) What is Gibbs Phenomena? 04
(c) Explain how to remove baseline drift in ECG using Digital filters. 07
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