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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. ii) ( 6 + z 1 ) X (z) = (1 + 0.25z 1 )(1 + 0.5z 1 ) b) Define Fourier Transform (FT), Discrete Time Fourier Transform (DTFT) and Discrete Fourier Transform (DFT). Find DFT of sequence x(n) = 1 for 0 n 2 = 0 otherwise For N = 4. Plot |X(k) | & LX(k). [8] Q4) a) Compare circular & linear convolution and find circular convolution of two find duration sequences x1(n) = {1, 1, 2, 3, 1} and x2(n) = {1, 2, 3} using concentric circle method. [8] b) What is FFT? Give classification of FFT. Explain Bit reversal and In Place computation concepts in FFT algorithm. Show 3-bit bit reversed sequence. [8] Q5) a) Obtain Direct form-II realization. i) 2 + z 1 + z 2 H (z) = (1 + 0.5z 1 )(1 1 z 1 )(1 + 1 z 1 ) 4 8 ii) [8] y (n) + 3 y (n 1) + 1 y (n 2) = x(n) + x(n 1) 4 8 b) Obtain IDFT for the DFT sequence given below. i) X(k) = {0, 0, 2, 0} ii) X(k) = {4, 5, 3, 5} [8] SECTION - II Q6) a) Explain following features and typical registers associated with following units of DSP Processor. [8] i) ALU. ii) MAC. iii) Barrel shifter. iv) Program sequencer. b) Explain frequency sampling technique of FIR filter design. [6] c) Draw block diagram of typical ADSP 21XX series Processor. [4] Q7) a) A first order low pass Butterworth transfer function with 3 dB cut off frequency at C is given by Ha(s) = C/(S + C). Design a single pole low pass digital filter with 3 dB bandwidth of 0.2 rad using BLT. Hence obtain H(w) and find values of H(w) at w = 0 and w = 0.2 . [8] [3664]-57 2 b) Explain Impulse Invariance Transformation and its drawback. Hence obtain the system function H(z) for the transfer function given below using Impulse Invariance Technique for T = 0.2 sec. [8] H(s) = 10 . (s 2 + 7s + 10) Q8) a) Design a FIR filter with H d ( w) = e jzw | w | / 4 =0 otherwise Use Hanning window with N = 7. [8] b) Explain Gibb s phenomenon and compare performance of different window function. [8] Q9) a) Explain Goertzel Algorithm in detail. [6] b) Compare FIR & IIR filters. Explain selection of a filter for a particular application. [6] c) Draw Butterfly diagram for 8 point DIF FFT complete in all respect.[4] Q10) a) Determine the step response for the LTI systems represented by following Impulse response. [8] i) h(n) = (n) (n 1) ii) h(n) = (1/2)n u(n) b) Explain in detail application of DSP in echo canceller or Speech Analysis. [8] [3664]-57 3

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