Visvesvaraya Technological University (VTU) 2006 B.E Electrical and Electronics Engineering 5th SEM DIGITAL SIGNAL PROCESSING - Question Paper
| USN |
| | |||||||||
|
NEW SCHEME | ||||||||||
Fifth Semester B.E. Degree Examination, July 2006 Electrical and Electronics Digital Signal Processing
Time : 3 hrs.] [Max. Marks ; 100
Note : 1. Answer any FIVE full questions.
1 a. Define the DFT and IDFT of a discrete time sequence x(n) of length N; Find x(0),
x() and x(N-k) if x(n) is real (10 Marks)
b. Give the periodic sequences x(n) = {1,3,5,7} and y(n) = {2,4,6.8] find their convolution using stockhams methods. (10 Marks)
2 a. Xi(k) and X2(k) are the DFTS of the discrete time sequences xj(n) and x2(n)
respectively, each of length N.
If Xj(k) = Xi(k) Xi(k), show that
N-1
X3(n) = -rn))Ni m = 0 to N-l. (10 Marks)
m=0
b. Given and infinite sequence input:
X(n) = { 1.2.3,4,1,J,5,7,2,4,6,8,.........}
and h(n) = {1,2.1}. Find the output y(n) using overlap - add method considering x(n) is made up of segments of length 4. (10 Marks)
3 a. What are FFT algorithms? Find the number of computations required to find the DFT
of an n point sequence using:
i) Direct meihod ii) DITFFT Algorithm
If N = 64, X = 68. (10 Marks)
b. Write a note on Butterfly structure as used in DITFFT and DIFFFT algorithms, with relevant equations represented by them. (10 Marks)
4 Given x(n) = {1.3,5.7,2,4,6,8} draw the SFG for finding its DFT using:
i) DITFFT Algorithm ii) DIFFFT Algorithm.
Hence find the DFT of x(n) by both the methods. " (20 Marks)
5 a. Explain the development of structures of realization using:
i) Direct Form I ii) Direct Form II.
Hence obtain there structures for a system described by the difference equation.
2y(n) + 0.2>\n-a) + 0.4y (n-2) + 0.6y (n-3) = 0.8x(n) + x(n-l) + 1.2x(n-2). (10 Marks) 3(2z2 +5z + 4)
b. Given H(z) = - for an HR system, obtain the parallel form of
(2z + l)(z + 2) y V
realization. (10 Marks)
6 a. What is linear Phase Characteristic? Show that a system for which h(n) = h(N-l-n),
Exhibits such a characteristic. (10 Marks)
b. GiveHfzO +z') (--ir"1 +-jz"z) for an FIR system, obtain the realization in
i) Direct Form ii) Cascade Form. (10 Marks)
Page So. 2 EE55 *
7 a. The desired frequency response for a linear phase FIR system having an impulse
response of finite length N, N being odd, is given by Hi(w) = eJTW for w < wc < n
o otherwise, with x = -.
2
o. . , , sin((/7 - r)w. )
Show that hd(n) = --. (10 Marks)
{n-r)n
b. Explain the concept of windowing in FIR filter design and describe the modified rectangular window and the Hamming window. (10 Marks)
8 a. Establish the Bilinear transformation between the s domain and the z domain.
Hence show that the region outside the unit circle in the domain corresponds to the right half of splane. (10 Marks)
b. Determine the order and poles of a Butter worth low pass filter that has a-3db bandwidth of 500Hz and an attenuation of 40 db at 1000 Hz. (10 Marks)
*****
|
Attachment: |
| Earning: Approval pending. |
