Question Paper: Discrete Time Signal Processing Question Paper - Dec 16 - Electronics And Telecomm (Semester 6) - Mumbai University (MU)
0

## 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.
(5 marks) 00

1(b) What are the advantages of digital filter over analog filter?
(5 marks) 00

1(c) State and prove frequency shifting property of DFT.
(5 marks) 00

1(d) Compare: FIR filter and IIR filter.
(5 marks) 00

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}

(10 marks) 00

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.

(10 marks) 00

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.
(10 marks) 00

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
(10 marks) 00

4(a) Design a Linear Phase FIR Low Pass filter of Length 7 and cut off frequency 1 rad/sec using Hamming window.
(10 marks) 00

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 marks) 00

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 $\pi$

(10 marks) 00

5(b) With a suitable block diagram describe sub-band coding of speech signals.
(10 marks) 00

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

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

(10 marks) 00

6(b) Write a note on Frequency Sampling realization of FIR Filter.
(10 marks) 00