26-09-2013, 12:48 PM
Digital Signal Processing Assignment 2
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1. a) How can you form DFT from DTFT ? Explain.
b) Deduce the relation in between DFT and Z-Transform.
c) Compute the DFT of x(n) = δ (n-n0) considering the length to be N.
d) Write down the comparison between DTFT and DFT.
e) What is Twiddle factor ? Explain how Twiddle factor exhibits the circular property for any number of points. (3x5)
2. a) Find 4-point DFT of x(n) = { 1 , -1 , 2 , -2 } directly.
b) Find the IDFT of X(k) = { 4 , 2 , 0 , 4 } directly.
c) Write down the properties of Twiddle factor. (5+5+5)
3. a) Find the DFT of a sequence : x(n) = 1 for 0 ≤ n ≤ 2 and 0 otherwise for N=8.
b) Write down the methods to find out circular convolution.
c) What are the differences in between circular convolution and linear convolution?
d) Find out the circular convolution by Matrix multiplication method in between the sequences x(n) = {1,-1,-2,3,-1} and
h(n) = {1,2,3}. (6+2+3+4)
4. a) Explain the Matrix formulation method of the DFT and IDFT.
b) Explain how IDFT can be computed by using DFT.
c) Find the DFT of the sequence x(n) = {1,-1,2,2} using Matrix formulation.
d) Find the IDFT of X(k) = {4,2,0,4} using DFT. (5+2+4+4)
5. a) How can you find linear convolution by using DFT ? Explain.
b) Find the linear convolution of the sequence x(n) and h(n) using DFT where x(n) = {1,2} and h(n) = {2,1} . Verify the result
by using any method of linear convolution.
c) Write short note on : Circular convolution. (4+7+4)
6. a) Determine the output response y(n) if h(n) = {1,1,1} and x(n) = {1,2,3,1} by using : (i) Linear convolution and
(ii) Circular convolution .
b) Compare the above two results. Explain
c) What should the measure to be taken to compute the result of linear convolution by using circular convolution?
d) Also find out the result of linear convolution by using circular convolution. (7+2+2+4)
7. a) What is sectioned convolution? Why is it required?
b) Write down the methods to find out sectioned convolution.
c) What are the applications of DFT?
d) What is zero padding? Why is it needed?
e) Why DFT is preferred over DTFT?
f) How IDFT can be computed from DFT? (3+2+2+2+3+3)
8. a) What do you understand by filtering of long duration sequences?
b) Write short note on : Overlap Save Method.
c) Find the output y(n) of a filter whose impulse response is h(n) = (1,1,1) and input signal x(n) = {3,-1,0,1,3,2,0,1,2,1} using
overlap save method. (2+5+8)
9. a) Write short note on : Overlap Add Method.
b) Find the output y(n) of a filter whose impulse response is h(n) = (1,1,1) and input signal x(n) = {3,-1,0,1,3,2,0,1,2,1} using
overlap add method.
c) State the differences between overlap add and overlap save method.