Download GTU BE/B.Tech 2019 Winter 7th Sem New 2171003 Digital Signal Processing Question Paper

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Seat No.:

Subject Code: 2171003

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Enrolment No.

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER- VII (New) EXAMINATION — WINTER 2019

Subject Name: Digital Signal Processing

Time: 10:30 AM TO 01:00 PM

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Instructions:

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

Q.1 (a) Define the following terms in context of signal processing: MARKS

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1. Period of discrete sinusoid,
2. Correlation of signals,
3. ROC of Z-transform.

(b) The system given below have input x(n) and output y(n). 03

y(n) = log {x(n)}

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Answer the followings with justification.

1. Is the system linear?
2. Is it time-invariant?
3. Is it stable?

(c) Draw & discuss typical block diagram of Digital Signal Processing 04

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(DSP). Explain any one example of DSP used in real-time application.

Q.2 (a) Explain the following terms in brief: 07

1. Minimum phase system.
2. Dirichlet’s Condition for existence of DTFT.

(b) State the relationship between Z-transform and Fourier transform. 03

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(c) Determine the step response of the causal system described by the 04

following LCCDE.

y(n) = y(n—1) + x(n)

OR

(a) Consider x(n) as input and y(n) as output of the system. 07

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Compute the linear as well as circular convolution of following

sequences:

x(n) = {1,2,0,1} and h(n) = {2,2,1,1} for 0 < n < 3

Comment on the results obtained.

(b) A liner time-invariant system is characterized by its impulse response 03

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h(n) = (1/2)ⁿ u(n)

Determine the spectrum and energy density spectrum of the output

signal when the system is excited by the signal.

x(n) = (1/3)ⁿ u(n)

(c) Compute the Z-transform of the following sequence. 04

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x(n) = aⁿ; 0 < a < 1

Draw Direct Form-I and Direct Form-II structures for the following

system function:

H(z) = (1 + 0.875z^-1) / ((1 + 0.2z^-1 + 0.9z^-2)(1 - 0.7z^-1))

Q.3 (a) Compute the DFT of the following four-point sequence using DFT 03

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matrix.

x(n) = {0,1,2,3}

(b) Consider the signal 04

x(n) = {—1, 2, 1/2 ,2, —1}

with Fourier transform X (w). Compute the following quantities, without

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explicitly computing X (w).

1. X(0)
2. X(p)
3. ?|X(?)|² d?

(c) List out the properties of DFT and prove the followings: 07

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1. Symmetry for real sequence
2. Time reversal

OR

Q.3 (c) Write down the properties of Z-transforms and prove the followings: 07

1. Time-shifting property

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2. Differentiation property

Q.4 (a) Enlist at least three differences between FIR and IIR Filters. 03

(b) Explain the followings in context of Multirate signal processing: 04

1. Decimation
2. Interpolation

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(c) Discuss the design of FIR filter using windowing method in brief. 07

OR

Q.4 (a) What do you mean by frequency wrapping? 03

(b) Explain the followings in context of DSP processor architecture: 04

1. MAC

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2. Pipelining

(c) Discuss design steps of IIR filter using bilinear transformation. 07

Q.5 (a) Compute the IDFT of the function X (w) = 2p d(w) 03

(b) Write a short critical note on adaptive filters and discuss any one 04

application of it.

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(c) Discuss in brief: Radix-2 Decimation-in-Time FFT algorithms. 07

OR

Q.5 (a) Determine the partial-fraction expansion of the proper function 03

X(z) = (z) / (z² + 1.5z + 0.5)

(b) Write a short critical note on Harvard architecture of DSP processor. 04

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(c) Explain in brief: The Goertzel Algorithm. 07

Date: 03/12/2019

Total Marks: 70