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Sixth Semester [B.Tech]  April 2006
Paper Code : ETEC – 306 Subject : Digital Signal Processing 
Time : 1^{1}/_{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). 
2.5 x 3 
( b ) 
The FIR filter of length N=11 has linear phase. Show that the
following condition is satisfied

5 
Q2 
( a ) 
For the given sequence calculate: 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 5point DFTs. Determine the sequence y(n) so that Y(k) = X1(k) X2(k) ? 
5 
Q3 
( a ) 
Find the 8pt DFT of the sequence using SR2 DIT FFT algorithm. x(n) = [ 1 2 3 4 4 3 2 1 ] and from the obtained result compute the sequence x(n) using SR2 DIF IFFT algorithm. 
5 + 5 
Q4 
( a ) 
Design an ideal band pass filter with a desired frequency response for N=11 
10 
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