A A7010

Total Pages: 2
Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIFTH SEMESTER B.TECH DEGREE EXAMINATION, DECEMBER 2017
Course Code: EC301
Course Name: DIGITAL SIGNAL PROCESSING

Max. Marks: 100 Duration: 3 Hours
PART A
Answer any two full questions, each carries 15 marks. Marks
1 ஐ Explain, how DFT and IDFT can be expressed as Linear Transformation (3)
b) Derive the relationship of DFT to Z-transform (3)
c) Find the circular convolution of x[n] = {1, 2, -1, 3, 4} and h[n] = (2, -1, 4, 1, 3} (5)
d) Explain overlap add method for filtering of long data sequences. (4)

2 a) Show that, if [1] is a real and even sequence, then its DFT X[k] is also real and (3)
even
b) Find linear convolution of x[n] (2, 3, -1} and h[n] = {1, -1, 2}, using circular (5)
convolution.
c) Find the number of complex multiplications involved in the calculation of a 1024 (3)
point DFT using (i) direct computation(ii) radix-2 FFT algorithm
d) Explain, how N point DFTs of two real-valued sequences can be found by (4)
computing a single N point DFT.
3 ஐ Find 8 point DFT of x[n] = {2, 1, -1, 3, 5, 2, 4, 1} using radix-2 decimation in time (11)
FFT algorithm
b) Explain, how ೩ 2N point DFT of a 2N point real-valued sequence can be found by (4)
computing a single N point DFT.

PART B
Answer any two full questions, each carries 15 marks.

4 a) Prove that, 1 21 is a zero of a linear phase FIR filter, then 1/2 is also a zero. (5)

b) Design a linear phase FIR low pass filter having length M = 15 and cut-off (10)
frequency നം = 7/6. Use Hamming window.

5 a) Explain the design of linear phase FIR filters by the frequency sampling method. (9)

b) Explain the frequency transformations in the analog domain (6)

6 Design a digital Butterworth low pass filter with രു = 7/6, ७६ = 7/4, minimum (15)

pass band gain = -2dB and minimum stop band attenuation = 8dB. Use bilinear

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