GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-VII (OLD) EXAMINATION — WINTER 2018
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Subject Code: 171704 Date: 29/11/2018
Subject Name: Digital Signals & Systems
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 (a) What do you understand by aliasing? How will you control aliasing? [07]
(b) What do you mean by sampling process? State the sampling theorem and explain the concept of sampling. [07]
Q.2 (a) Define periodic signal and fundamental period and Determine the signal X(t) = 2 cos (6pt — p/3) + 4 sin (10pt) is periodic ? If so find its fundamental period. [07]
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(b) For a given discrete time systems, check whether they are: (1) Static or dynamic (2) Linear or non-linear (3)Shift invariant or shift-varying (4)Causal or non-causal (5) Stable or unstable. i) x(n) ii) x(2n+9) iii) nx(n) [07]OR
(b) Find homogeneous solution of a given system difference equation: y(n) - 3y(n-1) - 4y(n-2) = x(n) ; y(-1)=5; y(-2)=0 [07]
Q.3 (a) Find the Z transform of x(n)=n2u(n) by the help of differentiation property. [07]
(b) List out properties of z transform. [07]
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OR
Q.3 (a) Draw and explain-block diagram of DSP. [07]
(b) Explain Low pass and High pass filter. [07]
Q.4 (a) Obtain the linear convolution by graphical method of following sequences. x(n)={1,4,3,2,1} and h(n) = { 1,2,1,2,1} [07]
(b) Compute the cross-correlation between x(n) = {1,2,3,4} and y(n) = {1,2,1,2} [07]
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OR
Q.4 (a) Draw parallel realization of IIR filter having transfer function H(Z)= (1-Z-1)/(1-0.2Z-1-0.15Z-2) [07]
(b) Explain direct form —I and direct form —II structure of IIR filter. [07]
Q.5 (a) Compute 4 point DFT of x(n) = {1,2,3,4} [07]
(b) List out properties of DFT. [07]
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OR
Q.5 (a) Explain forward DCT with necessary equations [07]
(b) Explain lattice structure of FIR filter [07]
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