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1997 Course Digital Signal Processing

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Total No. of Questions : 10] P1183 [Total No. of Pages : 3 [3664]-57 B.E. (Industrial Electronics) DIGITAL SIGNAL PROCESSING (1997 Course) (404221) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) 2) 3) 4) 5) 6) Answer any 3 questions from each section. Answers to the two sections should be written in separate books. Neat diagrams must be drawn wherever necessary. Figures to the right indicate full marks. Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. Assume suitable data, if necessary. SECTION - I Q1) a) Define stability. State & derive the condition for system to be stable in terms of impulse response. Test stability of the system whose impulse [6] response is h(n) = (1/2)n u(n) b) An analog signal xa(t) = 15 cos (1250 t) + 17 cos (2170 t) + 33 cos (4750 t) is converted into discrete time signal. Determine Nyquist sampling rate, folding frequency, resulting discrete time signal x(n), if sampling frequency is 625 Hz. Also write the discrete time frequencies in radians. [6] c) Compute & sketch convolution y(n) of following signals x(n) = 0.5n [6] (0 n 5) & h(n) = 1 ( 3<n< + 3). Q2) a) An LTI system is defined by difference equation y(n) = y(n 1) + y(n 2) + x(n 1). Find system function H(z). Draw pole-zero diagram. Find out h(n) for causal, non-causal system. Is the system stable in both cases? If not what should be h(n)? [8] b) Find convolution of following two signals using Z-transform. x1(n) = an u(n) & x2(n) = u(n) (Note : a < 1). Q3) a) Find the causal sequence x(n) for i) X (z) = [8] [8] 1 + 3z 1 (1 + 3z 1 + 2 z 2 ) P.T.O.

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