06000EC301122003 Pages: 2

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Max. Marks: 100

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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
Fifth Semester B.Tech Degree (S,FE) Examination January 2022 (2015 Scheme)

Course Code: EC301
Course Name: DIGITAL SIGNAL PROCESSING

PARTA
Answer any two full questions, each carries 15 marks.
Write down the equation for N point DFT and explain each term
Find N point DFT of unit impulse 6(12)
Find 4 point DFT of x(n) = [1, -2, 3, 2].
Find 4 point circular convolution of x(n) = h(n) = [1,1,1,1] using DFT.

Compute 8-point DFT of the sequence [1 1 1 1 0 0 0 0] using Decimation in Time
FFT algorithm
Let x(n) = {1,0,1,0} and h(n) = {1,2,2,1}. Find 4 point DFTs of these sequences
using a single 4 point DFT.
Find the IDFT of X(k) = [1,0,1,0] using DIF FFT algorithm.
PART B

Answer any two full questions, each carries 15 marks.
Prove that a symmetric impulse response results in a linear phase response for an
FIR filter with an even filter order N.
Compare main 3 properties of rectangular, Hanning and Hamming window
functions.
How filter order is selected in the window-based method of FIR filter design.
Explain impulse invariant mapping. List the main limitations of impulse invariant
mapping.
Design a Digital Butterworth filter to satisfy the constraints 0.9 > |H(w)|<
1:0 > ८ > 0.57. |H(w)| > 0.2; 0.757 < ¢ > 7. Use bilinear transformation.
Assume T=1 s.
Design a Linear phase LPF with a cut off frequency of 0.57 rad/s using frequency
sampling. Take N = 13, use type | design.
Derive the mapping function from s to z in Bilinear transformation. Explain

frequency warping.

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Duration: 3 Hours

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