GTU BE 8th Semester 182402 Digital Signal Processing Summer 2018 Question Paper

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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