Question Paper: Discrete Time Signal Processing : Question Paper May 2016 - Electronics & Telecomm (Semester 6) | Mumbai University (MU)
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## Discrete Time Signal Processing - May 2016

### Electronics & Telecomm. (Semester 6)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
1(a) Explain multirate signal processing with applications.(5 marks) 1(b) If h(n) = {1, 2, 3, 4} is impulse response of FIR Filter, Realize the filter in direct form.(5 marks) 1(c) State and prove Parseval's Theorem.(5 marks) 1(d) State advantages and disadvantages of digital filters.(10 marks) 2(a)(i) x(n) = {1, 2, 3, 4} find DFT of x(n)(5 marks) 2(a)(ii) Using results obtained in part (i) and otherwise find DFT of following sequences
a(n = {4, 1, 2, 3} b(n) = {2, 3, 4, 1} c(n) = {3, 4, 1, 2} d(n) = {4, 6, 4, 6}
(10 marks)
2(b) A digital filter is describe by the following differential equation y(n) = 0.9 y(n-1) + bx(n)
(i) Determine b such that |H (0)|=1
(ii) Determine the frequency at which |H(W)|=$\dfrac{1}{\sqrt{2}}$
(iii) Indentify the filter type based on the passband.
(10 marks)
3(a) If x(n) = {1, 2, 3, 4, 5, 6, 7, 8}, Find X(K) using DITFFT. Compare computational complexity of above algorithm with DFT.(10 marks) 3(b) Show the mapping from S plane to Z plane using Impulse Invariant Method and explain its limitation. Using this method, determine H(Z) if $$H(s)=\dfrac{3}{(s+2)(s+3)}\ \text {if} \ T=0.1\ \text{sec}$$(10 marks) 4(a) Design a Linear phase FIR Low Pass filter of Length 7 and cut off frequency 1 rad/sec using rectangular window.(10 marks) 4(b) If x(n) = {1, 2, 3, 2} and h(n) = {1, 0, 2, 0}
(i) Find circular convolution using time domain method.
(ii) Find linear concolution using circulat convolution,
(10 marks)
5(a) Design a digital Butterworth filter for following specifications using Bilinear transformation technique
Attenuation in Pass band = 1.93dB,
Pass band Edge frequency = 0.2π,
Attenuation in Stop band = 13.97dB,
Stop band Edge frequency = 0.6π,
(10 marks)
5(b) With a suitable block diagram describe sub-band coding of speech signals.(10 marks)

### Attempt the following

6(a) Short note on dval tone multifrequency detection using Geortzel's algorithm.(8 marks) 6(b) Compare FIR and IIR filters.(6 marks) 6(c) Finite word length effect in digital filters.(6 marks)