Anna University B.E. Computer Science and Engineering

V Semester

Digital Signal Processing

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**Part-A (10 x 2 = 20 Marks)**

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1. Represent the following discrete time signal in Z domain.

X(n) = {.6^{n }– 0 < n < 5

0 – otherwise

2. Draw the 8 point Radix DIT signal flow graph.

3. Write down the procedure for designing IIR filter.

4. Write the relationship between ‘S’ domain and ‘Z’ domain .

5. What is Gibb’s Phenomenon?

6. Write the expression for Kaiser window function.

7. Demonstrate the two types of cascade realization in implementation of filters.

8. Realize the filter 6(1-Z^{-1})/(1-5Z^{-1})

9. Give the relationship between auocorrelation sequence and power spectrum density of a discrete sequence and list out their use.

10. What is meant by upsampling show its implementation?

**Part-B (5 x 16 = 80 Marks)**

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11. i. Find h(n) for

H(Z) = z/ 3Z^{2}-4Z+1

ii. Given x_{1}(n) = {2,1,1,2}, x_{2}(n) = {1, -1, -1, 1}

Find the convolution of x_{1}(n) and x_{2}(n)

12 (a) Design a LPF with following specifications. Use Hamming window

and at least 8 points.

(b) Design and implement a linear phase FIR filter of length M = 15 which has the following unit sample response

H(2 k/15) = { 1 k = 0, 1, 2, 3

0 k = 4, 5, 6, 7}

13.(a) i. Obtain H(z) from H(s) when T = 1 sec.

H(s) =1/S^{2} + 2S +1

ii. Design a digital BPF using w1 & w2 as cutoff frequencies

H(s) =1/S^{2} + ?2S +1

(OR)

(b) i. Find H(s) for 3^{rd} order filter.

ii. Design a Chebyshev LPF filter for the following specification

Maximum pass band ripple = 1.2dB.

At W = 2.5 r/s, the loss is –30 dB at 1r/s.

14 (a) i. Discuss errors due to finite word length effect.

ii. Realize the following H(z) given by

H(Z)=(1+Z^{-1}) (1+2Z^{-1})/ (1+1/8Z^{-1})(1+1/2Z^{-1})(1+1/4Z^{-1})

using cascade and Parallel form with Direct form-I.

(OR)

(b) i. What is meant by quantization error? Explain briefly.

ii. Realize the following filter using cascade technique with

DF-I and DF-II.

H(Z) = 8Z^{3}-4Z^{2}+11Z-2/(Z-1/4 ()Z^{2}-Z1/2)

15(a) Briefly explain

i. Interpolator

ii. Decimator

iii. Effects due to sampling rate conversion

iv. Applications of multirate signal processing.

(OR)

(b) i. Briefly explain energy density spectrum, periodogram.

ii. Find periodogram for the following sequence using DFT.

{1,0,2,0,3,1,0,2}