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Digital Signal Processing 5th AM11 CS2403

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Fifth Semester
Information Technology
(Regulation 2008)

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PART A — (10 × 2 = 20 marks)

1. State sampling theorem.
2. Distinguish between power and energy signal with an example.
3. State and prove Parseval's theorem.
4. Compute the DFT of the four point sequence x(n ) = [0,1,2,3].
5. What is meant by warping?
6. What are the limitations of impulse invariance method?
7. List out the conditions for the FIR filter to be linear phase.
8. What is meant by limit cycle oscillations?
9. Let x(n ) = [1,2,-3,4,5,-6]. Sketch x (n 2) and x (3n ).
10. Give any two image enhancement methods.

PART B — (5 × 16 = 80 marks)

11. (a) (i) Suppose a LTI system with input x(n ) and output y(n ) is characterized by its unit sample response h(n ) (0.8) u(n ) = n . Find the response y(n ) of such a system to the input signal x(n ) = u(n ) .(8)
(ii) A causal system is represented by the following differenceequationnCompute the system function H (z ) and find the unit sample response of the system in analytical form. (8)
(b) (i) Compute the normalized autocorrelation of the signal x(n ) = a u(n ),0 < a <1 .="" br="" n="">(ii) Determine the impulse response for the cascade of two LTI system having impulse responses ( ) (1 / 2) ( ) 1 h n u n = n and ( ) (1 / 4) ( ) 2 h n u n = n . (8)

12. (a) By means of the DFT and IDFT, determine the response at the FIR filter with the impulse response h(n ) = [1,2,3] and the input sequence x(n ) = [1,2,2,1].
(b) Compute the DFT of the following sequence x(n ) using the decimation in time FFT algorithm x(n ) = [1,-1,-1,-1,1,1,1,-1].

13. (a) (i) Find the H (z ) corresponding to the impulse invariance design using a sample rate of 1/T samples/sec for an analog filter H (s) specified as follows : (6)
(ii) Design a digital low pass filter using the bilinear transform to satisfy the following characteristics (1) Monotonic stop band and pass band (2) - 3 dB cutoff frequency of 0.5 p rad (3) magnitude down at least -15 dB at 0.75p rad . (10)
(b) Design an IIR filter using impulse invariance technique for the given  . Assume T = 1 sec. Realize this filter using direct form I and direct form II. (16)

14. (a) Design and obtain the coefficients of a 15 tap linear phase FIR low pass filter using Hamming window to meet the given frequency response (16)
(b) (i) Determine the coefficients of a linear phase FIR filter of length M = 15 which has a symmetric unit sample response and a frequency response that satisfies the conditions
(ii) The output of A/D converter is applied to digital filter with the system function. Find the output noise power from the digital filter when the input signal is quantized to have 8 bits. (8)

15. (a) Derive and explain the frequency domain characteristics of the Decimator by the factor M and interpolator by the factor L. (16)
(b) With neat diagram explain any two applications of adaptive filter using LMS algorithm. (16)

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