Download GTU BE/B.Tech 2019 Winter 7th Sem Old 171003 Digital Signal Processing Question Paper

Enrolment No.

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER - VII • EXAMINATION - WINTER 2019

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Subject Code: 171003

Subject Name: Digital Signal Processing

Time: 10:30 AM TO 01:00 PM

Date: 28/11/2019

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.

1. (a) Perform the linear convolution of following sequences using graphical method. X[n]= {1,2,-1} and h[n] = {2,3,-2} [07]

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2. (b) State and prove the following properties of DTFT. (1) Frequency Shifting (2) Differentiation in Frequency [07]

1. (a) Explain the following properties of a discrete time system with suitable example. (1) Linearity (2) Causality (3) Time invariance [07]
2. (b) What is ROC in context of Z-transform? List various properties of ROC. [07]

1. (a) Define DTFT. Using DTFT, find impulse response of a LTI system described by difference equation y[n] — ¹/₂ y[n—1] = x[n] — ¹/₄x[n —2] [07]
2. (b) Find inverse Z-transform of following: X(z) = ¹/_{(1 + ¹/2z^-1) (1-2z^-1)(1 -3z^-1)} |z| > 3 [07]

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1. (a) Write short note on Structures for linear phase FIR systems. [07]
2. (b) Find Z Transform and ROC of following signals. (1) x[n] = naⁿu[n] (2) x[n] = (¹/₂)ⁿ u[n] — (¹/₃)ⁿ u[-n-1] [07]

1. (a) Draw Direct form-I and Direct form-II structures for the system whose system function is H(z) = ^2z2/_{(1 - ¹/4z^-1)} - ^(1-4z-1)/_{z (1 - ¹/2z^-1)} [07]
2. (b) What is circular convolution? How is it different from linear convolution? Determine the circular convolution of two sequences x(n) = cos(pn/2) for n=0,1,2,3 h(n) =2ⁿ for n=0,1,2 [07]

1. (a) Discuss frequency domain representation of sampling. [07]

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2. (b) With help of block diagram explain architecture of TMS320C6XXX processor. [07]

1. (a) Define DFT. Show relationship between DFT and DTFT. Prove any one property of DFT. [07]
2. (b) Describe the decimation in frequency algorithm, with the help of a flow graph, for 8-point DFT computation. [07]

1. (a) Explain windowing method of designing FIR filter. [07]
2. (b) Describe the decimation in time algorithm, with the help of a flow graph, for 8-point DFT computation. [07]

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1. (a) List the various methods of designing IIR filter. Explain IIR filter design using Bilinear Transformation method [07]

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