SRM University 2007 B.Tech Electronics and Communications Engineering BANK : EC303 – DIGITAL SIGNAL PROCESSING - Question Paper

24. Given x(n)={0,1,2,3,4,5,6,7}. obtain X(K) using DIF-FFT algorithm
25. Given x(n)= 2n and N=8. obtain X(K) using DIF-FFT algorithm.
26. Given x(n)= n +1 and N=8. obtain X(K) using DIF-FFT algorithm.
27. Compute the 8-point DFT of the sequence x(n) = {1,1,1,1,0,0,0,0}using DIT-FFT algorithm.
28. Given X(K)= { 20,-5.828- j2.414,0,-0.172-j0.414,0,-0.172 + j0.414,0,
-5.828 + j2.414}.Find x(n)
29. Given X(K)={ 255, 48.62+j166.05, -51+j102, -78.63+j46.05,-85,
-78.63-j46.05,-51-j102,48.62-j166.05}.Find x(n).
30. Given X(K) = {36,-4+j9.656,-4+j4,-4+j1.656,-4,-4-j1.656,-4-j4,
-4-j9.656} obtain x(n)
31. Find the DFT of the sequence x(n)={1,1,1,1,0,0,0,0} using DIT-FFT algorithm.
32. Find the DFT of the sequence x(n)={2,2,2,2,1,1,1,1} using DIT-FFT algorithm.
33. Find the DFT of the sequence x(n)={1,0,1,0,1,0,1,0} using DIT-FFT algorithm.
34. Find the IDFT of the sequence X(K)= { 4,1-j2.414,0, 1-j0.414,0,
1+j0.414, 0, 1+j2.414}using DIF-FFT algorithm.
35. Determine the direct form –II structure for the provided system
y(n) = ½ y(n-1)- ¼ y(n-2)+x(n)+x(n-1).
36. Realize the system with difference formula
y(n) = 3/4 y(n-1)- 1/8 y(n-2)+x(n)+1/3 x(n-1) in cascade form.
37. Obtain the DF-I,DF-II and cascade form realization for the subsequent system y(n)= -0.1 y(n-1)+0.2 y(n-2)+3x(n)+3.6x(n-1)+0.6x(n-2).
38. Determine Direct form I&II for the 2nd order filter provided by
y(n)= 2r cos? y(n-1) – r2 y(n-2)+x(n)- r cos? x(n-1).
39. Obtain the cascade realization for the subsequent system.
( 1+ 3/2 Z-1 +1/2 Z-2 ) (1-3/2 Z-1 +Z-2 )
H(Z) = -----------------------------------------------
( 1+ Z-1 +1/4 Z-2 ) (1+1/4 Z-1 +1/2 Z-2 )

1+3 Z-1
40.Find the inverse Z- transform of X(Z)= ------------------ ; ? Z ? >2 using
1+3 Z-1 +2 Z-2
partial fraction method.

Z(Z2-4Z+5)
41. obtain the inverse Z- transform of X(Z)= ------------------ ; for ROC
(Z -3)(Z-1)(Z-2)

i) two < ? Z? < three (ii) ? Z?> three (iii ) ? Z? < one using partial fraction method.

Earning:   Approval pending.