Reg 210.2 न 00000EC30112 19)nme:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
Fifth semester B.Tech degree examinations (S) September 2020

Course Code: EC301
Course Name: DIGITAL SIGNAL PROCESSING
Max. Marks: 100 Duration: 3 Hours
PARTA
Answer any two full questions, each carries 15 marks. Marks
1 a) Compute 5 point DFT of the sequence (17) = {1,1,1,1,1} (5)

b) Express DFT as a linear transformation. How many complex multiplications and (10)

additions are needed to compute N point DFT.

tN

a) Find the 4 point circular convolution of sequences x;(m) = {2,1,2,1} withx.(m)= (8)
(12.34)

0) Explain how to compute linear convolution of two sequences of length N; and (7)
N> using DFT.

3 a) Derive Decimation In Time (DIT) FFT algorithm for 8 point DFT and draw the (8)

signal flow graph.

b) Explain overlap and add method for filtering of long data sequences. (4)
c) Prove that N point DFT is periodic with period 77 (3)
PART B

Answer any two full questions, each carries 15 marks.
4 a) How the phase of a filter is related to frequency for a linear phase filter? Why (5)
linear phase is important in certain filtering applications?
b) Derive the condition for impulse response ॥(४) for getting a linear phase (10)
response. Assume length of (2) = N, an even number.
5 8) Derive the mapping between 9 and 2 used in bilinear transformation. (3)
b) Design a digital Butterworth filter satisfying the constraints (12)
0.6 > |H(e”)| > 1:0 > ७ > 0.357
| (९/५) | < 0.1; 0.77 < ८ 5 7. Use Bilinear transformation. Assume T= 0.1
6 a) Give equations for N point Hamming and Hanning Window functions. Compare (6)
them in terms of main lobe width and side lobe level.

b) Explain frequency sampling method of FIR filter design. (3)