8/14/2019 Nr410201 Digital Signal Processing Set1

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Code No: NR410201 NR

IV B.Tech I Semester Supplementary Examinations, February 2007DIGITAL SIGNAL PROCESSING

( Common to Electrical & Electronic Engineering and InformationTechnology)

Time: 3 hours Max Marks: 80

Answer any FIVE QuestionsAll Questions carry equal marks

1. (a) Show that a relaxed linear time invariant system is equal if and only if h(n)= 0 for n < 0.

(b) Determine the range of values of parameter a for the linear time invariantsystem with impulse response h(n), to be stable, where

h (n) =

an n > 0, n even0, otherwise

[8+8]

2. (a) A discrete system is given by the following difference equation:y(n)-5y(n-1) = x(n) + 4x(n-1)where x(n) is the input and y(n) is the out put. Find the impulse response.Determine its magnitude and phase response as a function of frequency.

(b) Show that the frequency response of a discrete system is a periodic functionof frequency. [8+8]

3. (a) Define DFT of a sequence x(n). Obtain the relationship between DFT andDTFS.

(b) Consider a sequence x(n) = {2,1, 1, 1} and T = 0.5 compute its DFT andcompare it with its DTDT. [8+8]

4. (a) Implement the Decimation in frequency FFT algorithm of N-point DFT whereN-8. Also explain the steps involved in this algorithm.

(b) Compute the FFT for the sequence x(n) = { 1, 1, 1, 1, 1, 1, 1, 1 } [8+8]

5. (a) How will you test the stability of a digital filter? Discuss the stability of thesystem described by H(Z) = Z

1

1Z1Z2

(b) Determine the frequency, magnitude and phase responses and time delay forthe system

y(n) +1

4y(n 1) = x(n) x(n 1) [8+8]

6. A digital low pass filter is required to meet the following specificationsPass band attenuation 1dbPass band edge 4 KHzStop band attenuation 40db, Stop band edge = 8KHzSample rate 24 KHzThe filter is to be designed by performing a bilinear transformation on an analogsystem function. Design a butter worth filter and realize it. [16]

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8/14/2019 Nr410201 Digital Signal Processing Set1

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Code No: NR410201 NR

7. (a) Design a low pass filter by the Fourier series method for a seven stage withcut-off frequency at 300 Hz if ts = 1msec. Use hanning window.

(b) Explain in detail, the linear phase response and frequency response propertiesof Finite Impulse Response filters. [8+8]

8. (a) What are the advantages in cascade and parallel realisation of IIR systems(b) The transfer function of a system is given by

H(Z) =(1 + Z1)

31 1

4Z1

1 Z1 + 1

2Z2

Realize the system in cascade and parallel structures. [6+10]

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