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2003 Course Advanced Digital Signal Processing (Elective I)

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Total No. of Questions : 12] P989 [Total No. of Pages : 3 [3664]-200 B.E. (E & TC) ADVANCED DIGITAL SIGNAL PROCESSING (Elective - I) (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answers to the two sections should be written in separate books. 2) Neat diagrams must be drawn wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. 6) Attempt Q.1 or Q.2, Q.3 or Q.4, Q.5 or Q.6 from Section - I. 7) Attempt Q.7 or Q.8, Q.9 or Q.10, Q.11 or Q.12 from Section - II. SECTION - I Q1) a) b) Find the power spectrum for each of the following WSS random processes that have the given autocorrelation sequences. [10] i) rx (k) = 2 (k) + j (k 1) j (k + 1). ii) rx (k) = (k) + 2(0.5)| k |. For a factor-of-L up sampler governed by xu(n) = x (n /L) for n = 0, L, 2L, obtain a Z-Transform equivalent relationship. [8] OR Q2) a) b) Q3) a) b) Define a Wide Sense Stationary (WSS) and Strict Sense Stationary (SSS) process. Every WSS process can be SSS but every SSS process may not be so explain. [8] Let x(n) be a random process that is generated by filtering white noise w(n) with a filter having system function H(Z) = (1/1 0.25 Z-1). The variance of the white noise is w2 = 1. Obtain the autocorrelation function rx (k). [10] Draw the block diagram of a typical adaptive filter. Explain the terms presented. [8] Justify the reason for considering mean square Error (MSE) cost function for adaptive algorithms in terms of its mathematical suitability and optimization of error. [8] P.T.O.

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