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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. OR Q4) a) Write down the generalized expression for gradient based adaptive algorithms, and explain the steepest descent algorithm with a neat sketch. [8] b) Compare and comment on the performances of the Least Mean Square (LMS) and Recursive Least Square (RLS) algorithm. [8] Q5) a) Explain what is an innovations process with the help of a neat sketch. [8] b) Consider an FIR filter with system function H(z) = 1 + 2.88 Z-1 + 3.4048 Z-2 + 1.74 Z-3 + 0.4 Z-4. Sketch the direct form and lattice realizations. One of the reflection coefficients will be observed to behave differently. Indicate which one and why. [8] OR Q6) a) Define and explain : i) AR ii) [8] MA and iii) ARMA processes. iv) For which type of process is the Toeplitz symmetry useful? b) Given a 3-stage lattice filter with coefficients K1 = 0.8, K 2 = 0.5, K3 = 0.14, determine the FIR filter coefficients with the direct form of structure. Sketch the direct form and lattice form structure. [8] SECTION - II Q7) a) Explain in detail the differences in parametric and non parametric methods of power spectral estimation. Indicate the limitations of the non-parametric method. Highlight with the help of example. [8] b) Determine the frequency resolution of the Bartlett method and Welch method of power spectral estimates for a quality factor Q = 10. Assume that overlap in Welch s method is 50% and the length of the sample sequence is 1000. [8] OR [3664]-200 2 Q8) a) b) Compare the salient features of Bartlett method and Welch method of power spectral density estimation. [8] Explain the terms periodogram and correlogram with neat sketches and examples. [8] Q9) Explain the following terms for a typical DSP processor (any 3) : a) Zero overhead looping. b) Circular buffering. c) Barrel shifter and it s role. d) Unique features of 218X / TMS 320C 6713 Processor. [18] OR Q10)a) Highlight the major differences between and application areas of fixed point DSP processor and floating point DSP Processor. [8] b) Justify the statement majority of the basic DSP operations are MAC . and Explain how the MAC block in a typical DSP processor implements the same efficiently. Enlist special instructions if any for any suitable DSP processor platform. [10] Q11)a) Describe the mechanism of human speech production with the help of a neat sketch. [10] Explain the meaning of the term format in the context of speech processing. [6] b) OR Q12)a) b) Explain how short time spectral analysis be used in the analysis of speech signals. [10] Explain the terms briefly : [6] i) Channel vocoders. ii) Sub band coding. vvvv [3664]-200 3

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