Download GTU B.Tech 2020 Winter 7th Sem 2171003 Digital Signal Processing Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER-VII (NEW) EXAMINATION - WINTER 2020

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Subject Code:2171003
Subject Name:Digital Signal Processing
Time:10:30 AM TO 12:30 PM

Instructions:

1. Attempt any FOUR questions out of EIGHT questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q1 (a) Compare the direct form-I and II structures of an IIR systems, with M-zeros and N-poles. MARKS 03
(b) Calculate the percentage saving in calculations in a 512-point radix-2 FFT, When compared in direct DFT. MARKS 04
(c) Draw and explain architectural block diagram of TMSC6000 DSP processor. MARKS 07

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Q2 (a) Give any three properties of Butterworth lowpass filters. MARKS 03
(b) Give the equation specifying Kaiser window. List the advantages of Kaiser window. MARKS 04
(c) Design a single-pole lowpass digital filter with a 3-db bandwidth of 0.2p, using the bilinear transformation applied to the analog filter
H(s) = O / (s + O)
Where O is the 3-dB bandwidth of the analog filter. MARKS 07

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Q3 (a) List the application of an adaptive filter. Briefly explain any one of it. MARKS 03
(b) Realize the following FIR system with minimum number of multipliers. h(n)={-0.5, 0.8, -0.5} MARKS 04
(c) Determine all the FIR filters which are specified by the lattice parameters
K₁=0.5, K₂ =0.6, K₃ = -0.7 and K₄ = 0.25 MARKS 07

Q4 (a) Determine a direct-form realization for the following linear phase filter. h(n) = {1,2,3,4,3,2,1} MARKS 03

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(b) Find the inverse DFT of Y (k)= {1,0,1,0}. MARKS 04
(c) Derive the signal flow graph for the N= 16-point, radix-4 decimation-in-time FFT algorithm in which the input sequence is in normal order and the computations are done in place. MARKS 07

Q.5 (a) Determine the inverse Fourier transform of X(e^j?) = 2pd(? — ?₀), |?₀| < p. MARKS 03
(b) Determine the inverse of the system with impulse response h(n) = (1/2)ⁿ u(n). MARKS 04
(c) Determine |H(?)|² for the system y(n) =-0.1y(n-1)+0.2y(n-2) + x(n) + x(n - 1). MARKS 07

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Q.6 (a) Determine the energy density spectrum of the signal x(n) = aⁿu(n), —1 < a < 1 MARKS 03
(b) Prove the Parseval’s relation ?_n=-8⁸ |x(n)|² = 1/(2p) ?_-p^p |X(e^j?)|² d? MARKS 04
(c) Determine the particular solution of the difference equation y(n) = 0.25y(n-1) - 0.125y(n-2)+x(n) When the forcing function x(n) = 2ⁿ, n > 0 and zero elsewhere. MARKS 07

Q.7 (a) Find the z-transform of naⁿu(n). MARKS 03
(b) Test the stability of the following systems.

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1. y(n) = cos[x(n)] MARKS 04
2. y(n)=x(-n-2)
(c) Find the response of the time invariant system with impulse response h(n) = {1,2,1,-1} to an input signal x(n) = {1,2,3,1}. MARKS 07

Q.8 (a) Determine the regions of convergence of right-sided, left-sided, and finite-duration two-sided sequences. MARKS 03
(b) An analog ECG signal contains useful frequencies up to 100Hz.

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I. What is the Nyquist rate for this signal?
II. Suppose that we sample this signal at a rate of 250 samples/s. What is the highest frequency that can be represented uniquely at this sampling rate? Justify your answer. MARKS 04
(c) Determine the inverse z-transform of X(z) = 1 / ((z-0.5)(z-1)) when ROC is |z| < 0.5 and |z| > 1. MARKS 07

Date:30/01/2021
Total Marks: 56

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