Categories: 8th Semester

1

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE – SEMESTER ?VIII (old) – EXAMINATION ? SUMMER 2018

Subject Code:182402 Date:30/04/2018

Subject Name:Digital Signal Processing

Time:10:30 AM to 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 (a) Compare Analog and digital signal processing in tabular form. 04

(b) state whether the following signal is an Energy or power signal.give

Justification for your answer:- x(n) = (0.5)

n

* u(n)

04

(c) What is the importance of ROC in z transform? State & prove any two the

properties of Linear convolution.

06

Q.2 (a) Define sampling. State and explain sampling theorem. 07

(b) Differentiate continuous and discrete valued signal. For an analog signal

x (t) = 3cos50pt + 10sin300 pt – cos100 pt. Calculate Nyquist rate.

07

OR

(b) Define stable system. Check whether the following system functions are

memory-less, stable, causal, linear and time-invariant or not. (1) y(n) = sign[x(n)] (2) y(n) = Trunc[x(n)]

07

Q.3 (a) State Parseval?s relation for DTFT. Also prove it. 07

(b) Find convolution of two sequences x(n) = (-1)

n

*

u(n) and h(n) = u(n) 07

OR

Q.3 (a) Explain the interconnection of LTI systems. 07

(b) State the properties of Discrete Fourier Transform (DFT) and prove the Time

Reversal property of DFT.

07

Q.4 (a) What do you understand by twiddle factor? Derive the relationship between

DFT and Z Transform.

07

(b) Explain following. (1) Radix-2 FFT algorithm (2) DIT algorithm 07

OR

Q.4 (a) (1) obtain the value of x(4) for 8 Point DFT if x(n) = { 1, -1, 0, 2, 1, -2, -1, 1}

? (2) Find out the circular convolution of x(n) = {1,2,3,4} and h(n) = {1,1,2,2}

07

(b) Determine the value of signal x(n) at n=0 and n=8 if,

X(z) = _______2______

Z

2

+ 1/6*Z – 1/6

07

Q.5 (a) Explain the structures for realization of FIR systems. 07

(b) Explain the following terms with respect to Digital Signal Processor: (1) Pipelining (2) MAC

07

OR

Q.5 (a) What are the different formats of fixed point representation? Explain the fixed

point representation of binary numbers.

07

(b) What do you understand by scaling? Discuss the effect of round-off in the

digital filter.

07

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