DIGITAL SIGNAL PROCESSING (utu previous year question paper)

DIGITAL SIGNAL PROCESSING
SEM-V, 2011,12
B.TECH EXAMINATION
UTTARAKHAND TECHNICAL UNIVERSITY
(UTU)

Time: 3 hours

Total marks:100

Section A

Answer any four parts of the following:

1. What do you understand by digital signal processing? Explain the advantage and application of digital signal processing.
2. Find the response of an FIR with impulse response h[n] = [1,2,4] to the input sequence x[n] = [1,2] using Linear transformation method.
3. State and prove the following properties of DFT.
   (a) Circular time reversal
   (b) Circular time shift
4. Compute circular periodic convolution of the two sequences x₁[n] = [1,1,2,2] and x₂[n] = [1,2,3,4] using DFT & IDFT method.
5. State and prove "circular convolution" property of DFT.
6. Compute N point DFT of
   x(n) = {1,1,2,2,3,3} and compute the corresponding amplitude and phase spectrum.

 Section B

Answer any four parts of the following :

1. State the relationship between DTFT and DFT.
2. Determine the DFT of the sequence:
   
3. Determine the IDFT of X[k] =[3,(2+j), 1,(2-j)].
4. Draw the butterflyline diagram for 8 point IFFT calculation and briefly explain.
5. Given x[n] = {0,1,2,3,4,5,6,7} and N =8, find X[k] using DIT FFT algorithm. 
6. Given x[n] =₂n and N = 8 find X[k] using DIF FFT algorithm.

Section C

Answer any two parts of the following :

1. Develop a canonic direct form realisation IIR transfer function
   
   
   And then determine its transpose configuration.
2. Draw the structures of cascade and parallel realization of
   
3. What are linear phase FIR filter? How can the symmetry of these filter help to simplify the network structure? Realize the following casual linear phase FIR system function
   H[z] = 1+ 2.88 z^-1 + 3.404 z^-2 + 1.742 z^-3 + 0.4 z^-4.

Section D

Answer any two parts of the following :

1. What do you mean by frequency warping? Convert the analog filter with system function
   
   
   Into a digital IIR filter using bilinear transformation. The digital filter should have a resonant frequency of
   w_r  = π/4
2. A low pass filter is to be designed with the following desired frequency response
   
   
   Determine the filter coefficient h_d (n) if the window function is defined as
   
3. What is a Kaiser window? In what way is it superior to other window function? Explain the procedure for designing an FIR filter using the Kaiser window.

Section E

Answer any two parts of the following :

1. Explain in details the uses of adaptive filter. What is meant by Echo cancellation? Explain in details.
2. What do you mean by Winear filter? Draw Winear filter characteristics. Also write drawback of Winear filters.
3. Write short note on the followings:
   (i) Discrete cosine transform
   (ii) Walsh-Hadamard transform.

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