## Discrete Time Signal Processing - Dec 16

### Electronics And Telecomm (Semester 6)

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 phase delay and group delay.

**1(b)**What are the advantages of digital filter over analog filter?

**1(c)**State and prove frequency shifting property of DFT.

**1(d)**Compare: FIR filter and IIR filter.

**2(a)**

(i) x(n) = {1,2,3,4} find DFT X(k)

(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 described by the following differential equation.

$$ y(n) = 0.9 y(n-1) + b x(n) $$

(i) Determine b such that $|H(0) | = 1$

(ii) Determine the frequency at which $|H(w)| = \frac{1}{\sqrt(2)}$

(iii) Identify the filter type based on the passband.

**3(a)**If x(n) = { 1 0 2 0 3 0 4 0}. Find X(K) using DIFFFT. Compare computational complexity of above algorithm with DFT.

**3(b)**Explain effect of aliasing in Impulse Invariant Technique. Using this method, determine $H(Z)$, if $H(s) = \frac{3}{(s+2) (s+3)}$ if T=0.1 sec

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

**4(b)**if x(n) = {1,2,3,2} and h(n) = {5,6,7,8}

a) Find circular convolution using time domain method.

b) Find circular convolution using DFT/IDFT method.

c) Find linear convolution using circular convolution.

**5(a)**Design a digital Butterworth filter for following specifications using Bilinear Transformation Technique.

Attenuation in Pass band = 1.93 dB, Pass band Edge frequency = 0.2 $\pi$

Attenuation in Stop band = 13.97 dB, Stop band Edge frequency = 0.6 $\pi$

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

**6(a)**Determine FIR lattice coefficient of system with transfer function.

$$ H(Z) = 1 + \frac{13}{24}Z^{-1} + \frac{5}{8}Z^{-2} + \frac{1}{3}Z^{-3}$$

**6(b)**Write a note on Frequency Sampling realization of FIR Filter.