## 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)