Question Paper: Discrete Time Signal Processing Question Paper - May 16 - Electronics And Telecomm (Semester 5) - Mumbai University (MU)

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## Discrete Time Signal Processing - May 16 (Old Credit Based Grading System)

### Electronics And Telecomm (Semester 5)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

**1(a)**Explain multirate signal processing with applications.

**1(b)**If h(n) = {1, 2, 3, 4} is impulse response of FIR Filter, Realize the filter in direct form.

**1(c)**State and prove Parseval's Theorem.

**1(d)**State advantages and disadvantages of digital filters.

**2(a)(i)**x(n) = {1, 2, 3, 4} find DFT of x(n)

**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}

**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.

**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.

**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 $$H(s)=\dfrac{3}{(s+2)(s+3)}\ \text {if} \ T=0.1\ \text{sec}$$

**4(a)**Design a Linear phase FIR Low Pass filter of Length 7 and cut off frequency 1 rad/sec using rectangular window.

**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,

**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,

**5(b)**With a suitable block diagram describe sub-band coding of speech signals.

Q6) Attempt the following:

**6(a)**Short note on dval tone multifrequency detection using Geortzel's algorithm.

**6(b)**Compare FIR and IIR filters.

**6(c)**Finite word length effect in digital filters.