Download GTU BE/B.Tech 2019 Winter 5th Sem New 2150307 Digital Signal Processing Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER- V (New) EXAMINATION - WINTER 2019

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Subject Code: 2150307 Date: 06/12/2019

Subject Name: Digital Signal Processing

Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

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

Q.1 (a) Define Signal. Explain briefly classification of Signals. 03

(b) Determine whether following signals are periodic or not: 04

1. x1(t) = sin15wt

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2. x2(t) = sin20 mt
3. x3(t) = sinv2 mt
4. x4(t) = x1(t) + x2(t)

(c) Explain in detail the overall block diagram of Digital Signal processing system. 07

Q.2 (a) Enlist properties of Z-Transform and prove any two properties of it. 03

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(b) Give definition of following terms: 04

1. Energy Signal
2. Power Signal
3. Sampling Theorem
4. Quantization Error

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(c) Determine the z — transform of sequence given by: 07

2ⁿ, n<0

x(n) = (¹/₂)ⁿ, n=0

(¹/₃)ⁿ ,n=1,3,5

OR

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(c) Find x (n) for given transfer function using PFE method and also validate your answer using long division method. 07

X(2) = (2+3z^-1) / (1+z^-1)(1 - ¹/₂z^-1)

Q.3 (a) Prove any three properties of DFT. 03

(b) Compute Linear convolution of following given sequence using mathematical method 04

X(m)={1,1,0,1, 1} & h(n)={1,-2,-3, -4}

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(c) Find the inverse DFT of following response 07

X(k)={1,2,3, 4}

OR

Q.3 (a) Explain briefly application of Goertzel algorithm. 03

(b) Determine I'xx & I'xy for following sequences: 04

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x(m)={1,2,1,1} & y(m)={1, 1,2,1}

(c) Given x(n) = 2ⁿ and N = 8, find X (k) using DIT FFT algorithm. 07

Q.4 (a) Explain in brief the Cascade representation of Digital IIR system giving one example. 03

(b) Develop Direct form — I realization of following system: 04

H(z) = (0.28z^-1 + 0.319z^-2 + 0.04) / (1 - 0.63z^-1+ 0.32z^-2 - 0.172z^-3)

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(c) Design and FIR digital filter to approximate an ideal low pass filter with pass band gain of unity, cut off frequency of 850Hz and working at sampling frequency of fs = 500Hz. The length of impulse response should be 5. Use rectangular window function 07

OR

Q.4 (a) Explain Parallel realization of digital system giving suitable example. 03

(b) Obtain Direct form — II realization of following system 04

H(z) = (0.56z^-1 + 0.638z^-2 + 0.08z^-3) / (1+0.62z^-1+0.34z^-2 - 0.42z^-3)

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(c) Convert the analog filter with system function 07

H(s) = (s+0.1) / (s²+0.2s+9)

into a digital IIR filter using bilinear transformation. The digital filter should have a resonant frequency of w_r = p/4

Q.5 (a) Differentiate Analog filter and Digital Filter 03

(b) Explain briefly analysis of Cardiac Variability in context on signal processing. 04

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(c) Explain IIR filter design using Bilinear Z — Transform method. Also prove the transformation process stability. 07

OR

Q.5 (a) Explain how Laplace transform and Z — transform are related by their poles plot diagram? 03

(b) Explain briefly the fundamentals approach for detection of QRS complex wave from ECG signal using signal processing. 04

(c) Explain IIR filter design using (i) Approximation of derivatives and (ii) Impulse Invariance method. 07

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