November 2010 BE CSE 6C0107 Digital Signal Processing Sathyabama University

Register Number

                               

SATHYABAMA UNIVERSITY

(Established under section 3 of UGC Act, 1956)

Course & Branch: B.E-CSE

Title of the Paper: Digital Signal Processing         Max. Marks: 80

Sub. Code: 6C0107                                                 Time: 3 Hours

Date: 20/11/2010                                                    Session: AN

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PART - A                (10 X 2 = 20)

Answer ALL the Questions

1.     State sampling theorem.

2.     What is BIBO stability?

3.     What is casual system?

4.     Write down the expressions for discrete time unit impulse and unit step functions.

5.     How many multiplications and additions are required to compute N-point DFT using radix-2 FFT?

6.     Compute Linear Convolution

         x(n) = {1,31,3}

         h(n) = {1,2,1}

7.     Mention two transformations to digitize an analog filter.

8.     Define rectangular window function.

9.     What is truncation error?

10.   What is meant by limit cycle oscillation?

PART – B                       (5 x 12 = 60)

Answer All the Questions

11.   (a) If a system is represented by the following difference equation

        Y (n) = 3y² (n-1) – nx (n) + 4x (n-1) – 2x(n+1) ³ 0

(i)                         Is the system linear? Explain.

(ii)                     Is the system shift invariant? Explain.

(iii)                  Is the system casual? Why or why not?

(b) A LTI system has an impulse h(n) = αⁿu (n), êα ê< 1. Determine the output of the system when the input x(n) = u(x)

(or)

12.   (a) What are the advantages of DSP over ASP?

        (b) Define and plot the following signals: (i) ramp, (ii) step and (iii) impulse

       

13.   For the stable and causal system described by y(n) + 0.1y(n-1) + 0.2y(n-2) = x(n-1) + x(n)

        (a) Determine H(z)

        (b) Determine h(n)

        (c) Determine the response to unit-step input.

(or)

14.   Obtain parallel realization using first and second order sections for the transfer functions.

        H(z) = [2(z-1) (z²+1.414z+1)] / [(z+0.5) (z²-0.9z+0.81]

15.   Obtain the linear convolved output y(n)=x(n)*h(n), using circular convolution, given that x(n) = {1,1,0,-1,-1}, h(n) = {1,2,3,2,1}

(or)

16.   Compute the DFT of the sequence x(n) = (1 if 0 £ n £ 7; 0 otherwise) by using DIT – FFT algorithm. Sketch the magnitude and phase spectrum.

17.   From H_a(s) = 2 / [(s+1) (s+4)], determine H(z) using impulse invariant method for (a) t=1 sec, (b) t = 0.1 sec.

(or)

18.   Explain the design of FIR filter using frequency sampling technique.

19.   (a) What are the effects of finite word length?

        (b) What is zero limit cycle oscillations? Explain.

(or)

20.   Explain the characteristics of limit cycle oscillation with respect to the system described by the difference equations

y(n) = 0.95y(n-1) + x(n). Determine the dead band of the filter.

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