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Posted By: India Member Level: Diamond Posted Date: 06 Jun 2008
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2008 Jawaharlal Nehru Technological University Electrical and Electronics Engineering IV B.Tech I Semester Supply Examinations, February 2008 (E.E.E) Question paper
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Code No: RR410201 Set No. 1
IV B.Tech I Semester Supplimentary Examinations, February 2008
DIGITAL SIGNAL PROCESSING
(Electrical & Electronic Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Consider a LSI system with unit sample response h(n)n = anu(n) where a is
real and 0 < a < 1 . If the input is x(n) = ßn u(n), 0 < |ß| < 1 ,determine the
the output f(n) in the form y(n) = (k1an + k2ßnu(n) by explicitly evaluating
the convolution sum.
(b) Define causality and stability of LSI system and state the conditions for sta-
bility.
[12+4]
2. Consider two periodic sequences x(n) and y(n), x(n) has period N and y(n) has
period M. The sequence w(n) is defined as w(n) = x(n) + y(n).
(a) Show that w(n) is periodic with period MN.
(b) Determine W(K) in terms X(K) and Y(K) where X(K), Y(K) and W(K)
are the Discrete Fourier series coefficients with a period of N, M and MN
respectively. [8+8]
3. (a) State and prove the circular time shifting and frequency shifting properties of
the DFT.
(b) Compute the circular convolution of the sequences
x1(n) = {1, 2, 0, 1} and
x2(n) = {2, 2, 1, 1} Using DFT approach. [8+8]
4. (a) Implement the Decimation in frequency FFT algorithm of N-point DFT where
N-8. Also explain the steps involved in this algorithm.
(b) Compute the FFT for the sequence x(n) = { 1, 1, 1, 1, 1, 1, 1, 1 } [8+8]
5. (a) Explain how the analysis of discrete time invariant system can be obtained
using convolution properties of Z transform.
(b) Determine the impulse response of the system described by the difference
equation y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1) using Z transform. [8+8]
6. (a) Find the order and poles of a low pass Butterworth filter that has a -3db
bandwidth of 500 Hz and an attenuation of 40db at 1KHz.
(b) Convert the following analog filter with transfer function
H(S) = S + 0.1/(S + 0.2)2 + 9 into a digital IIR filter by using bilinear
transformation method. The digital IIR filter is having a resonant frequency
of Wr = p/2. [8+8]
1 of 2
Code No: RR410201 Set No. 1
7. (a) Design a band stop filter to reject frequencies in the range 1-2 radians/second
using rectangular window N=7
(b) Write the magnitude and phase function of FIR filter when impulse response
is anti symmetric and N is odd function. [8+8]
8. (a) Obtain the cascade and parallel form realisation of the LTI system governed
by the equation.
(b) Compare cascade and performance of direct and canonic forms. [12+4]
? ? ? ? ?
2 of 2
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