1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
PDDC SEMESTER- VI • EXAMINATION SUMMER-2017
Subject Code:X61103 Date: 04/05/2017
Subject Name: Digital Signal Processing
Time: 10.30AM to 01:00PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 What is aliasing in discrete time systems? What is the solution to avoid it? 07
Consider a system with impulse response
. The input is anu(n).Find the output of the system.
07
Q.2 Consider a system x(n).Find the output of the system with the
input recursive method.
07
Enlist the symmetry properties of the Fourier transform. 07
OR
Prove the following Fourier transform theorems:
(i)Frequency shifting (ii)Differentiation (iii)Modulation
07
Q.3 Obtain the z-transform of the following

an 0 n N-1
07
Explain the properties of Region of Convergence of the z-transform. 07
OR
Q.3 Obtain the inverse z-transform of the following:
1 z-1 1
z-1
07
Discuss the types of structures for linear phase FIR filter. 07
Q.4 Draw the Direct form-I, Direct form-II,Cascade and Parallel form structures for
the following system:
1 z-1
07
What is windowing in FIR systems? Discuss the various window functions. 07
OR
Q.4 Design a low pass Butterworth Digital filter with the following specifications.
Use Impulse invariance method:


0 .8 9 1 2 5 1 0 0 .2
0 .1 7 7 8 3 0 .3
j
j
H e
H e






07
Discuss the limit cycle because of round off and overflow in IIR system. 07
Q.5 Prove the linearity and circular shift property of the Discrete Fourier Transform. 07
Find the 4-point circular convolution of the following sequences:


07
OR
Q.5 Compare (i)FIR and IIR filter (ii)Causal and Non causal System. 07
Write a short note on the applications of digital signal processing. 07