2010 nov

Reg. No. :

44

Question Paper Code : 53110

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B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2010Fifth SemesterInformation Technology

CS 2403 DIGITAL SIGNAL PROCESSING(Regulation 2008)Time : Three hours

Maximum : 100 Marks

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Answer ALL questionsPART A (10 2 = 20 Marks)1.

Calculate the minimum sampling frequency required for x(t ) = 0.5 sin 50 t

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+ 0.25 sin 25 t , so as to avoid aliasing.

State any two properties of Auto correlation function.

3.

Write down DFT pair of equations.

4.

Calculate % saving in computing through radix 2, DFT algorithm of DFTcoefficients. Assume N = 512.

5.

What are the limitations of Impulse invariant method of designing digitalfilters?

6.

Draw the ideal gain Vs frequency characteristics of :

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2.

(b)

BPF.

Compare FIR filters and FIR filters with regard to :(a)

Stability and

(b)

Complexity

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4

7.

HPF and

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(a)



Represent decimal number 0.69 in fixed point representation of lengthN = 6.

9.

Prove that up sampling by a factor M is time varying system.

10.

State a few applications of adaptive filter.

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8.

PART B (5 16 = 80 Marks)11.

(a)

(i)

Find the convolution x (n) * h(n) , wherex (n) = a n u(n )h(n ) = n u(n )

(ii)

Find the Z-transform of the following sequences :x (n) = (0.5) n u(n ) + u(n 1)

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x ( n ) = ( n 5) .

Or

12.

(a)

(i)

State and explain sampling theorems.

(ii)

Find the Z-transform auto correlation function.

(i)

Explain, how linear convolution of two finite sequences are obtainedvia DFT.

(ii)

Compute the DFT of the following sequences :

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(b)

(1)

x = [1, 0, 1, 0]

(2)

x = [ j, 0, j,1] when j = 1 .

Or

13.

Draw the flow chart for N = 8 using tadix-2, DIF algorithm for findingDFT coefficients.

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(b)

(a)

Design digital low pass filter using Bilinear transformation, Given that

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Ha( s ) =

1.( s + 1)( s + 1.732 s + 1)

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Assume sampling frequency of 100 rad/sec.Or

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Design FIR filter using impulse invariance technique. Given thatHa( s ) =

1( s + 5s + 6)

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(b)

and implement the resulting digital filter by adder, multipliers anddelays Assume sampling period T = 1 sec.14.

(a)

Design the first 15 coefficients of FIR filters of magnitude specification isgiven below :H ( e jw ) = 1, / w / < / 2

= 0, otherwise.Or(b)

Draw THREE different FIR structures for the H(z) given below:

15.

(a)

(i)

A signal x (n ) = {6,1, 5, 7, 2,1}Find :(1)

x (n / 2)

(2)

x (2n ) .

Explain any one application using multirate processing of signals.

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(ii)

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H ( z ) = (1 + 5z 1 + 6z 2 )(1 + z 1 ) .

Or

Write short notes on the following :(i)

Adaptive filter

(ii)

Image Enhancement.

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(b)

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2010 nov

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