Visvesvaraya Technological University (VTU) 2007 B.E Electrical and Electronics Engineering 5th SEM DIGITAL SIGNAL PROCESSING - Question Paper

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Fifth Semester B.E. Degree Examination, July 2007 Electrical and Electronics Engineering Digital Signal Processing

Time: 3 hrs.]    [Max. Marks: 100

Note : Answer any FIVE full questions.

1    a. Compute the DFT of the 8 point sequence

xtnlJ¹ ; "ⁿ"³

[0 ; 4<;n<7

also determine the DFT of the following sequence without explicitly computing y(k) using basic equation.

fO ; 0 < n < 1

y[n] = jl;2<nS5    (10 Marks)

[0 ; 6 < n < 7

b. By means of DFT and IDFT, determine the response of the FIR filter with impulse response

h[n] = [1,2] with the input x[n] = [1, 2, 3] take N = 4.    (10 Marks)

N-l

2    a. Compute the quantity xj[n] X2[n] for the following sequences, using DFT

n=0

properties. Take N = 4.

271

Xi[n] = x₂[n] = cosn; 0<n<N-l    (12Marks)

N

b. Prove the following properties of DFT

i)    Circular frequency shift

ii)    Circular time shift

iii)    Parsevals theorem    (08 Marks)

3    a. The sequence x[n] = [1, 2, 3, 3, 2, 1, -1,-2, -3, 5, 6, -1, 2, 0, 2, 1] is filtered through a

filter whose impulse response is h[n] = [3, 2, 1, 1]. Compute the output of the filter y[n] using overlap and save method. Use 9 point circular convolution. (10 Marks) b. Determine the 8 point DFT for the signal x[t]= sin 314 t using DIF FFT flow chart.

(10 Marks)

4    a. Develop a radix 3 DIT FFT algorithm for evaluating the DFT for N = 9. (10 Marks)

b. Given

x(k) = [20,-5.828-j2.414, 0,-0.172-j0.414, 0,-0.172 +j0.414, 0,-5.828 + j2.414] find x[n] using IFFT algorithm.    (10 Marks)

Conld.... 2

5 a Obtain cascade and parallel structure for the system described by

y[n] + 0.1y|n - I]-0.72y[n - 2] = 0.7x[n]-0.252x[n -2]    (12 Marks)

b. Obtain the direct form realization of the linear phase FIR system given by

H(Z) = 1 HZ H--Z Z "* + Z    (08 Marks)

4 8    4    ^v

6    a. Explain impulse invariance method of transforming an analog filter into an

equivalent digital filter.    (08 Marks)

b.    Apply bilinear transformation to obtain digital low pass filter to approximate

H(S) =    . Assume cutoff frequency of 100 Hz and sampling frequency

S² +V2S+I

of 1 kHz.    (06 Marks)

c.    Explain the principle features of Harward architecture.    (06 Marks)

7    a. Design a digital low pass filter using Butterworth approximation to meet the

following specifications Pass band edge = 120 Hz Stop band edge = 170 Hz Stop band attenuation =16 dB.

Assume sampling frequency of 512 Hz. Use bilinear transformation. (10 Marks) b. Design a digital Chebyshev filter using bilinear transformation to meet the following specifications.

i)    3 dB ripple in pass band 0 < |co| < 0.3ti

ii)    20 dB attenuation in the stop band 0.6tt < |<o] < 7t

Use bilinear transformation.    (10 Marks)

8 a. The desired frequency response of a low pass filter is given by H_d(co) = e-i³ jc|<

= 0 < I CD I < 7T

4 Determine the frequency response of the FIR filter, if a Hamming window is used with N = 7.    (10 Marks) b. Design an ideal band pass filter with frequency response H_d (to) = 1 for 3 71 < | co | <  Use rectangular window with N = 11 in your design. (10 Marks)

4    4

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Earning:   Approval pending.