GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-V (NEW) EXAMINATION - SUMMER 2019
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Subject Code: 2150307 Date: 17/06/2019Subject Name: Digital Signal Processing
Time: 02:30 PM TO 05:00 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) Give the statement of “Sampling Theorem”. Explain briefly the errors 03
arises during sampling process.
(b) Justify the statement giving mathematical proof “Any signal can be 04
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expressed using summation of two signal parts where one part is evensignal and the other part is odd signal”.
(c) Define Signal Processing. Differentiate between Analog signal 07
processing and Digital signal processing, and also list out the
applications of Digital Signal Processing.
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Q.2 (a) State the Properties of Z — Transform. 03
(b) Define following terms: 04
1. Convolution 2. Correlation 3. Quantization 4. Aliasing
(c) Determine Z — Transform of following sequence: 07
1. x(n)={1,2,4,5,0,7}
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2. x(n)={1,2,4,5,0,7}OR
(c) Obtain Inverse Z — Transform of following function using PFE method 07
and also comment on its ROC
X(Z) =
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Q.3 (a) Enlist the properties of DFT with necessary mathematical equation. 03
(b) Compute Linear -convolution of following given sequence using 04
mathematical method
x(n)= {1, 1,1} & h(n)={1,1,1,1}
(c) Calculate 8 point DFT of: 07
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x(n)={1,2,1,2}OR
Q.3 (a) Write short note on Goertzel algorithm. 03
(b) Determine I'xx & I'xy for following sequences: 04
x(n)={1,1,0,1} & y(n)={4,-3, -1, 1}
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(c) Explain radix — N/2 DIT FFT algorithm with necessary diagram. 07
(a) Explain the effects of coefficient quantization in brief 03
giving one example.
(b) Develop Direct form — II realization of following system: 04
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H(z) = (3+3.6Z-1+0.6Z-2) / (1+0.1Z-1+0.2Z-2) (c) Design a linear phase FIR low pass filter of seventh order with cutoff 07
frequency 1 rad/sec using rectangular window.
OR
Q.4 (a) State the difference between Cascade and Parallel realization of digital 03
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system giving suitable example. (b) Obtain Direct form — I realization of following system 04
y(n) — (1/2)y(n -1)+(1/4)y(n -2)=x(n) + (1/3)x(n -1)
(c) Determine transfer function of digital filter using Impulse Invariance 07
method at 5Hz sampling frequency for given below H(s),
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H(s) = 1/(s +2)Q.5 (a) Compare IIR filter and FIR filter. 03
(b) Explain detection of Alpha waves, Beta waves and Gamma waves 04
using signal processing techniques.
(c) Explain IIR filter design using Bilinear Z — Transform method. 07
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OR
Q.5 (a) Explain mapping of s — plane and Z — plane with neat diagram. 03
(b) Explain in brief cardiac arrhythmias detection. 04
(c) What is windowing? Explain in detail the process of converting IIR 07
system in to FIR system using rectangular window method.
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This download link is referred from the post: GTU BE 2019 Summer Question Papers || Gujarat Technological University
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