Download GTU BE/B.Tech 2018 Winter 7th Sem Old 171003 Digital Signal Processing Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER-VII (OLD) EXAMINATION — WINTER 2018

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Subject Code: 171003 Date: 26/11/2018

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) A discrete-time signal x(n) is defined as 07

x(n) =
1+ -3<n<1

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a) Determine its value and Sketch the signal.

b) Sketch the signal if

I. First fold x(n)and then delay the resulting signal by four samples

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II. First delay x(n) by four samples and then fold the resulting signal

¢) Compare above results. Is folding and Delay Operation is commutative operation?

d) Can you express the signal x(n) in terms of §(n) and u(n) ?

(b) For each of following system determine whether system is stable, causal, 07 Linear, Time invariant or not.

L y(n) = S x(k)

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2. y(n) = x(n²)

3. y(n) = logx(n)

Q.2 (a) Prove that convergence of absolute sum of the impulse response is a sufficient 07 condition for BIBO (boundedinput bounded output) stability of LTI system.

(b) Obtain a linear convolution of following two discrete-time signals: 07

x(n) = S d(n—1) where k=0 to 2

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h(n) = 2?n[u(n) — u(n — 3)]

OR

(b) Enlist Properties of linear convolution. 07

Obtain linear Convolution for x(n) = {1,1,2,1,1} and h(n) = {1,-2, -3,2}

Q.3 (a) What is ROC? Explain the properties of ROC in Z-Transform. 07

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(b) Find magnitude Response and Phase Response of system described by 07 differential equation

y(n) - ?y(n - 1) =x(m) - ½x(n -1)

OR

(a) Obtain Direct Form I and Direct Form II realization of the following transfer function. 07

H(z) = (3+3.6z?¹+0.6z?²)/(1+0.1z?¹-0.2z?²)

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(b) Prove differentiation property of Z-transform and obtain the Z-transform of 07 nu(n) using the same.

Q.4 (a) The system function of the analog filter is given as 07

H(s)= (s+0.1)/((s+0.1)²+9)

Obtain the system function of the IIR digital filter by using impulse invariance method.

(b) State and Prove following Properties in terms of DFT. 07

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1. Time Reversal
2. Periodicity

OR

Q.4 (a) Compare FIR and IIR filters. 07

(b) Determine the response of FIR filter using DFT if 07 x(n) = {1,2} and h(n) = {2,3}

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Q.5 (a) Explain Decimation in Time FFT algorithm. 07

(b) Derive the DFT of the sample data sequence x(n) = {1,1,2,2,3,3} determine the 07 corresponding amplitude and phase spectrum.

OR

Q.5 (a) Explain multiplier-Accumulator (MAC) hardware in DSP processors. 07

(b) Discuss the applications of digital signal processing with suitable examples. 07

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