M. Tech. I (First) Semester Examination 2013-14
Course Code: MEC104 Paper ID: 0971215
Digital Signal Processing and Application
Time: 3 Hours Max. Marks: 70 Max Marks: 75
Note: Attempt six questions in all. Q. No. 1 is compulsory.
Assume suitable data for missings, if any.
1. Answer any five of the following (limit your answer in 50 words). (4x5=20)
a) Define a shift invariant system with suitable example.
b) Write the differentiation property for Z transform.
c) Why Discrete Fourier Transform is preferred over Discrete Time Fourier Transform?
d) What is the difference between recursive and non recursive filters?
e) How the aliasing effects are eliminated?
f) What is the basic difference between linear and circular convolution?
g) What do you mean by an anti-imaging filter?
h) Under what conditions a finite duration sequence h(n) will yield constant group delay in its frequency response characteristics and not the phase delay?
2. An LSI system is described by the difference equation. (10)
Specify, the region of convergence (ROC) of H(z), and determine h(n)for the following conditions:
a) The system is stable
b) The system is causal
3. Compute the Inverse Discrete Fourier Transform (IDFT) of the sequence:
X(K) = {7,−0.707 − j0.707,− j,0.707 − j0.707,1,0.707 + j0.707, j,-0.707+j0.707}. using DIT (radix-2) algorithm. (10)
4. Perform circular convolution of the following sequences using DFT and IDFT: (10)
x (n) {1,2,1,2} 1 = and x (n) {4,3,2,1}.
5. Design an ideal low-pass filter with N=11 with a frequency response. (10)
If the window function is defined as
6. Obtain an analog Butterworth filter transfer function that satisfies the following specifications:
Pass band gain = 0.5 db, Stop band gain = 3.0 db
Pass band frequency = 0.5 rad/sec, Stop band frequency = 1.5 rad/sec. (10)
7. The analysis filter Ho(z) in a two-channel Quadrature Mirror Filter (QMF) has the transfer function. (10
H (z) = 1+ z-1
a) Determine the polyphase filters P0(z2) and P1(z2).
b) Determine the analysis filter H1(z).
c) Determine the synthesis filters G0(z) and G1(z).
d) Show that the QMF bank results in perfect reconstruction
8. Write short notes on any two of the following: (5+5)
a) Applications of multirate signal processing
b) Oversampling in analog to digital (A/D) conversion
c) Fast Fourier Transform Algorithm