Visvesvaraya Technological University (VTU) 2007 B.E Electrical and Electronics Engineering 5th SEM DIGITAL SIGNAL PROCESSING - Question Paper
USN
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 Hd(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 Hd (to) = 1 for 3 71 < | co | < Use rectangular window with N = 11 in your design. (10 Marks)
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Earning: Approval pending. |