DIGITAL SIGNAL PROCESSING

DIGITAL SIGNAL PROCESSING
SEM-V,2012-13
B.TECH EXAMINATION
UTTARAKHAND TECHNICAL UNIVERSITY
(UTU)

Time: 3 Hours 

Total Marks: 100

SECTION - A

Attempt any four parts of the following:

1. If two discrete - time LTI systems are cascaded, then prove or disprove that interchanging their order does not change the total system.
2. Test the following systems are stable or not:
   (i) y(n) = cos[x(n)]
   (ii) 
3. Derive the condition for impulse response of causality and stability properties in LTI systems.
4. Differentiate between DTFT and DFT.
5. Differentiate between FFT and DCT.
6. Discuss about the application of adaptive filtering in echo cancellation.

SECTION - B

Attempt any four parts of the following:

1. Describe the following properties of Z-transform: 
   (i) Time - reversal 
   (ii) Time - shifting.
2. Compare the computational complexity of N- point DFT and N- point FFT algorithms. Under what conditions, computational complexity of DFT algorithms is simplified.
3. Discuss the merits and demerits of impulse invariance method.
4. Discuss about the Gibbs phenomenon in FIR filters.
5. Find out the transfer function of Hilbert transform in z-domain.

SECTION - C

Attempt any two parts of the following:

1. Find the 4-point FFT of x(n) = (1, 0, 1, 1) using decimal in time algorithm. Draw the Butterfly Diagram. Also compute the number of complex multiplications and additions and compare with that obtained for 4- point DFT.
2. Determine the causal signal x(n) whose Z- transform is given by
   
3. Design a Butterworth analog low-pass filter using Bilinear transformation with 1 - db pass-band ripple , pass-band edge frequency 2000 π radians per second , stop - band frequency 1000 π radians per second and minimum stop band ripple of 40 - db .

SECTION - D

Attempt any two parts of the following:

1. Find the DTFT of a rectangular pulse
   
2. Find out the Z-transform of following signal
   
3. The desired impulse response of a certain FIR low pass filter is given by
   
   Let the sampling rate is 10 kHz. Use Hamming window and compute the impulse response of the FIR filter.

 SECTION - E

Attempt any two parts of the following:

1. Discuss about the Goertzel algorithm in detail.
2. Explain in detail about the Chirp Z-algorithm.
3. Discuss about MPEG coding standardization.

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