Visvesvaraya Technological University (VTU) 2007 B.E Electrical and Electronics Engineering 5th SEM .06/.07 DIGITAL SIGNAL PROCESSING - Question Paper

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Fifth Semester B.E. Degree Examination, Dec.06/Jan. 07 Electrical and Electronics Engineering Digital Signal Processing Time: 3 hrs.]    [Max. Marks:100

Note: Answer any FIVE questions.

1 a. Determine 8 point DFT of the sequence x(n) = { 1, 1, 1, 1 }. Sketch its magnitude and phase spectra.    (10 Marks)

b.    Find N point DFT of the sequence x(n) = e*^wmn. 0 < n S N-l.    (05 Marks)

c.    5 samples of the 8 point DFT X(K) are X(0) = 0.25, X(l) = 0.125 - j 0.3018, X(6) = X(4) = 0, X(5) = 0.125 - j 0.0518.    (05 Marks) Determine the remaining samples, if the sequence x(n) is real valued sequence.

1 a. g(n) and h(n) are two sequences of length 6. They have 6 point DFTs G(k) and H(k) respectively. G(n) = { 4.1, 3.5, 1.2, 5, 2, 3.3 }

The DFTs G(k) and H(k) are related by circular frequency shift as H(k) = G((k-3))e. Determine h(n) without computing IDFT.    (08 Marks)

b. A long sequence x(n) is filtered through a filter of impulse response h(n) to give output y(n). Compute y(n) using overlap add technique. Given x(n) and h(n)as follows x(n)={l,2, 0, -3,4, 2,-1, 1,-2, 3,2, 1,-3}

h(n) = {1,1,1}. Use 6 point circular convolution.    (12 Marks)

a.    Given x(n) = n+1 and N = 8, determine x(k) using DIF - FFT algorithm. Mark all intermediate outputs and write all necessary equations.    (10 Marks)

b.    Derive and draw the complete decimation - in time (D1T) signal flow graph to compute DFT of a 6 point sequence. Mark all intermediate outputs and write corresponding computations.    (10 Marks)

a. Realize the system function H(Z) in cascade and parallel form. H(Z)=    (Z-<XZ-2)(Z+|)Z

Wi+ 4 z- M i N 1 I*- l z + L V2 2 JJ 2 2)\ L 4J L 4J

b. Realize the FIR filter having impulse response

b(n) = 5(n)-i S (n-l) 5 (n-2) + i 5 (n-3) - i S (n-4) + 5 (n-5). Use minimum number of multipliers.

5 a. Design a Butterworth analog highpass filter that will meet the following specifications : i) maximum pass band attenuation = 2dB

ii)    Pass band edge frequency = 200 rad/sec.

iii)    Minimum stop band attenuation = 20dB

iv)    Stop band edge frequency - 100 rad/sec.    (10 Marks)

Contd... 2

b. Determine the system function H(z) of the lowest order chebyshev filter that meets the following specifications.

i)    3 dB ripple in the pass band 0<|W|<0.37t.

ii)    At least 20 dB attenuation in the stop band O.671 < W < n.

Use Bilinear transformation.    (10 Marks)

a.    Explain Impulse Invariant Transformation.    (08 Marks)

b.    A digital low pass filter is required to meet the specifications :

20 log |H(w)| w=o.2n > - 1.9328 dB.

20 log |H(s)| o.6n < - 13.9794 dB.

Filter must have a maximally flat frequency response. Find H(Z) using Impulse invariant transformation.    (12 Marks)

a.    A filter is to be designed with the following desired frequency response.

Hd(w) = 0 - < w <  ^w 4 4

= e^j2w < w < n

4

Find the frequency response of the FIR filter designed using rectangular window.

W_R(n) =1 0 < n < 4

= 0 otherwise.    (10 Marks)

b.    A low pass filter has the desired frequency response

Hd(w) = Hd(e*^w) = e-j3w 0 < w < ti/2 = 0    it/2 < w < n.

Determine h(n) based on frequency sampling technique. Use N = 7. (10 Marks)

Write notes on:

a.    DSP architecture (TMS 320 c5 x processes )    (08 Marks)

b.    Advantages and disadvantages of frequency sampling design.    (₀₆ Marks)

c.    Advantages and disadvantages of IIR and FIR filters.    (₀₆ Marks)

*****

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Earning:   Approval pending.