(Please write your Roll No. immediately)

Roll No. ..................................

Time : 1¹/₂ Hours

Maximum Marks : 30

Note : Attempt any 3 questions in all. Q1 is compulsory. Each question carries 10 marks.

Q1

( a )

State and prove the following properties of Discrete Fourier Transform (DFT).
a) Circular Frequency Shift
b) Circular Convolution
c) Time reversal

2.5 x 3

( b )

Q2

( a )

For the given sequence calculate:
a) Circular convolution
b) Linear convolution

h(n) = [ 1 2 3 4 ]          x(n) = [ 1 2 2 1 ]

using circular shift.

5

( b )

Consider the folowing sequences

x1(n) = [ 0 1 2 3 4 ]          x2(n) = [ 0 1 0 0 0 ]

and their 5-point DFTs. Determine the sequence y(n) so that Y(k) = X1(k) X2(k) ?

Q3

( a )

x(n) = [ 1 2 3 4 4 3 2 1 ]

and from the obtained result compute the sequence x(n) using SR-2 DIF IFFT algorithm.

5 + 5

Q4

( a )

10