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1997 Course Digital Signal Processing & Application

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Total No. of Questions : 10] P1588 [Total No. of Pages : 3 [3764]-1042 B.E. (Electronics) DIGITAL SIGNAL PROCESSING & APPLICATION (404203) (1997 Course) Time : 3 Hours] [Max. Marks :100 Instructions to candidates : 1) Answer any 3 questions from each section. 2) Answers to the two sections should be written in separate books. 3) Neat diagrams must be drawn wherever necessary. 4) Figures to the right indicate full marks. 5) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 6) Assume suitable data, if necessary. SECTION - I Q1) a) What is stability of system? Explain stability criteria for LTI system. Also explain the same in terms of Z - domain. [6] b) Explain three properties of convolution. c) Test the following systems for time invariance, causality & linearity. i) y(n) = 5nx2(n) ii) [6] y(n) = 3x( n + 4) iii) y(n) = cos (x(n)). Q2) a) [6] Find the response of the system described as [8] y(n) y(n 1) = x(n) for i) ii) b) x(n) = u(n). x(n) = 2 n u(n). State convolution property in Z - domain & explain its advantage. Find convolution of signal using Z.T. [8] x1(n) = (0.25)n u(n 1) x2(n) = [1 + 0.5n] u(n). P.T.O. Q3) a) Compute 8 point DFT of sequence 1 1 1 1 , x(n) = , , , , 0 , 0 , 0 .0 2222 Using the inplace Radix-2 decimation in time algorithm. Follow exactly the corresponding signal flow graph & keep track of all intermediate variables. [8] b) Bring out difference between fourier transform & discrete fourier transform. State formula for DFT & IDFT and hence calculate IDFT of following sequence. X(k) = {4, 1 j, 2, 1 + j}. [8] Q4) a) What is ROC? What is its importance? Find ROCs of different finite & infinite duration non-causal sequences. [10] Determine the direct form I & II realization of the following LTI system. 2y(n) + y(n 1) 4y(n 3) = x(n) + 3x (n 5). [6] b) Q5) a) b) Determine circular convolution using stockham s method (DFT IDFT approach) for following sequence: [8] x1(n) = {2, 1, 2, 1} x2(n) = {1, 2, 3, 4} Explain following: [8] i) Overlap add and overlap - save method. ii) Antialiasing filter. SECTION - II Q6) a) The desired frequency response of a low pass filter is given by d ( ) = e j 2 =0 4 otherwise Design the filter using Hann window for N = 5 and also find out equation for ( ) . [8] b) Explain windowing technique of FIR filter design in detail. Also explain Gibb s phenomena and how it can be reduced. State different types of windows used with their window function & shape. [10] [3764]-1042 2 Q7) a) Explain impulse invariance transformation and its draw back. An analog filter has transfer function. H(s) = 10 (s + 7s + 10 ) 2 Design a digital filter equivalent to this using. Impulse invariance method for T = 0.2 sec. [8] b) For the given specification design an digital Butterworth filter using BLT. [8] Ap = 2 dB p = 20 rad / sec As = 10 dB s = 30 rad / sec Q8) a) With a neat block diagram explain the architecture of DSP processor. Compare it with micro-processor. [8] b) Explain application of DSP in digital image processing with atleast on actual application case. [8] Q9) a) b) Explain the relationship between fourier and Z - transform. [6] Write formula for convolution & correlation. How does convolution program differ from correlation. Find out the convolution & correlation of following sequences: { } h (n ) = {1, 2, 1} x (n ) = 1, 2, 3, 2, 1 [10] Q10)a) b) Obtain Direct form I & II realization of following system. y(n) + 0.1 y(n 1) 0.72 y(n 2) = 0.7 x(n) 0.95 x(n 2) [10] Explain freqn transformation in IIR filter design. [6] Y [3764]-1042 3

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