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1997 Course Digital Signal Processing & Applications

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Total No. of Questions : 10] [Total No. of Pages : 3 [3664] - 51 P 1340 B.E. (Electronics) DIGITAL SIGNAL PROCESSING & APPLICATIONS (1997 Course) (404203) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates: 1) Answer any three 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) Your answers will be valued as a whole. 6) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 7) Assume suitable data, if necessary. SECTION - I Q1) a) Determine the cross correlation sequence Yxy(1) of the following sequences : [10] { y ( n ) = { 1, 2, 0.5, 0, 0.........} } x ( n ) = .......0, 0, 1, 2, 0,3, 1, 0, 0...... b) Also find normalized cross correlation sequence pxy(1). Explain terms : i) Cross correlation, ii) Auto correlation. [8] Q2) a) b) c) State and explain autocorrelation properties. Explain sampling theorem. The DT-LTI system is characterized by the difference equation : y(n) = 3x(n) 4x(n 1) + 7/2y(n 1) 3/2y(n 2) Determine the impulse response of the system for : i) The stable system. ii) The causal system. Realize the system in direct 2 form. [4] [2] [10] Q3) a) If x(n) = u(n) u(n 2), find the DC component of this signal. Justify [8] your answer. P.T.O. b) Using first order sections, obtain cascade realization for [8] 1 + 1 z 1 1 + 1 z 1 4 2 H( z ) = 1 1 z 1 1 1 z 1 1 1 z 1 4 8 2 Q4) a) b) c) Compute the Z.T. and plot the ROC of : i) x(n) = n2u(n) ii) x(n) = Arn cos(w0n + )u(n). [2] [4] Given X(Z) = Z ( Z 1) 2 and H(Z) = 1 / (Z 1). Find IZT of both x(n) and h(n) and then using convolution sum y(n) = x(n) * h(n), find y(n). [6] Determine the time-domain signal for all possible cases if [4] 2 z 2 + 5z + 6 4z 5 H( z ) = + + ( z + 1)3 ( z + 1) 2 ( z + 1) Q5) a) b) Draw clearly with all notations Butterfly diagram for the following : i) 8 point FFT with DIT. ii) 8 point FFT with DIF. [8] Develop a decimation-in time FFT algorithm using 4-point DFTS for the case N = 4v. Compare the number of multiplications with the algorithms using 2-point DFTS with N = 22v. [8] SECTION - II Q6) a) Design a digital Butterworth filter satisfying the constraints 1 2 < = H ( e jw ) <= 1 [12] for 0 < = w < = 2 H ( e jw ) < = 0.2 for 3 4 < = w < = b) Q7) a) with a T = 1 sec using the bilinear transformation. Realize the filter using the most convenient realization form. Draw and explain the Direct Form - II structure for IIR system. [6] Explain the no of memory locations and computation required in each case above. Given the desired transfer function of LPF as [10] H d ( w ) = 1 for 2 <= w <= 2 = 0 elsewhere Find corresponding hd(n) and using Hamming and Hanning window find out h(n). The length of the window is 11. [3664] - 51 -2- b) c) Compare FIR filters and IIR filters. [4] Why is it not possible to realize the Ideal Low Pass Filter practically? [2] Q8) a) b) What do you understand by the term Adaptive Filter ? [2] Compare different window functions used in FIR filter design. State the mathematical function of each window function. [8] Write a short note on application of FFT. [6] c) Q9) a) b) Discuss salient features of architecture for TMS 320 XX/ADSP 21XX series DSP processor and functional blocks. [8] What is circular buffering? Why is it desired in typical DSP computations? Write a sequence of instructions to ensure circular buffering for an array of length 10. [8] Q10)a) b) Explain in detail Image Processing with at least one actual application. [8] Explain the role of DSP in speech signal processing briefly. [8] [3664] - 51 -3-

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