*ME054*

Second Semester M.E. (Control and Instrumentation) Degree Examination, June/July 2015 (2K8 Scheme) CI 211 : DIGITAL SIGNAL PROCESSING AND APPLICATIONS Time : 3 Hours

Max. Marks : 100

Instruction : Answer any five full questions. 1. a) Show that the unit impulse response h(n) of an LTI system used to evaluate the following : i) Input-output relation. ii) Frequency response of the system iii) Stability.

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b) Prove that the sampling of Fourier transform of a sequence x(n) results in N point DFT using which both the sequence and the transform can be reconstructed. 10 2. a) If x(n) is an even length sequence with an N-point DFT X(K), then determine the N-point DFT of the following in terms of X(K).

(

)

i) y(n) = x(n) – x n − N 2 .

(

ii) y1(n) = x(n) + x n + N

2

).

6

b) Discuss the properties of R.O.C. of z-transform.

4

c) Find the impulse response of an LTI system, in closed form, if the system

(

)

function is given by H(z) = loge 1 + a z −1 |z| > a.

10

3. a) Find the impulse response of a set of LTI systems, if its system function is given by H(z) =

z+2 for all possible ROC’s. 2z − 7z + 3 2

10

b) State and prove the following properties of DFT. i) Circular Frequency Shift. ii) Circular convolution in Time domain. iii) Linearity.

10 P.T.O.

*ME054*

ME – 054

4. a) Illustrate the Radix-2 decimation in frequency FFT Algorithm, with necessary mathematical analysis and discuss its computational benefits over direct computation of DFT. 12 b) Compute the response of FIR filter for the following data using DFT-IDFT approach : x[n] = {2 1 1 2 } h[n] = {3 4 1 2}

8

5. a) Derive expression of poles from the squared magnitude response of Butterworth Low Pass Filter.

6

b) Explain the bilinear transformation method of Digital Filter Design.

6

c) Using impulse invariance method, design digital filter from analog prototype that has a system function Ha (s) =

s+ 2 . (s + 3) (s + 1)

8

6. a) Differentiate FIR and IIR filter characteristics.

10

b) Design an FIR Band pass filter of length 9 for the following characteristics :

( )

H e jω = 0

for

0 ≤ | ω | ≤ 0.4 π

=1

for

0.4π ≤ | ω | ≤ 0.6 π

=0

for

0.6π ≤ | ω | ≤ π

Use Hamming window.

10

7. Write explanatory note on the following : i) Parametric Spectral Estimation. ii) Multi-rate signal processing iii) DSP applications in RADAR and speech signal processing.

_______________________

(6+6+8)