IT6502 Digital Signal Processing, Third year, Departmentof Electrical & Electronics Engineering, First and second Units Questions
PART A – (10 x 2 = 20 Marks)
1. What is
Aliasing ?. How is it corrected ?.
2. Test the
stability of the system y(n) = cosx(n) ?.
3. Define even
and odd signals ?.
4.
State and
prove parseval’s theorem?.
5. Find the energy and power of x(n) = Aejωnu(n).
6. What are the
applications of FFT algorithm ?.
7. Define
Twiddle factor? .
8. Differentiate DIT-FFT & DIF-FFT algorithm ?.
9. Write down
DFT pair of equations.
10.
Determine the number of multiplications required in the computation of 8-point
DFT using
FFT ?.
PART
B-(5 x16=80 Marks)
11.a)
(i) State & prove sampling theorem.
(10)
(ii) State & prove any two
properties of z-transform. (6)
12.a)
Determine the z-transform for the sequence.
(i)
x (n) = 4ncos[ + ] u(-n-1)
(4)
(ii) x(n) = [-1/5]n u(n) +
5[1/2]-n u(-n-1) (4)
(iii) x(n) = u(n-2)
(4)
(iv) Find the inverse Z-transform of
X(Z) = 1/ ( 1−1.5 𝑍−1+ 0.5 𝑍−2) if ROC : |Z|
> 1, (4)
13.i)
Check whether the following systems are Static or Dynamic, Linear or
Non-linear, Time variant or invariant, Causal or non-causal, Stable or
unstable.
(i) y(n) = Cos[x(n)] ii) y(n) = x(-n+2)
(iii) y(n) = x(2n) iv) y(n) =
x(n)Cosωn
(10)
(ii) Convolve the sequence
i) x(n) = ( ) n u(n) & h(n) = ( )n
u(n)
(3)
ii) x1 (n) =
{-1,2,3,4,5} & x2(n) = {
6,7}
(3)
14.
Find DFT of the sequence x(n) = {1,2,3,4,4,3,2,1} using radix-2 DIT-FFT &
DIF-FFT
Algorithm.
(16)
15.
(i) Compute the DFT of the four – point sequence x(n) = {0,1,2,3}. (8)
(ii) Find the IDFT of the sequence Y(k)
= {1,0,1,0}.
(8)
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