### Digital Signal Analysis and Processing, 2065 Baisakh-Old - Old questions

TRIBHUVAN UNIVERSITY
INSTITUTE OF ENGINEERING
Examination Control Division
Full Marks:
80
Pass Marks
30
Time
3 hrs.

### Digital Signal Analysis and Processing, 2065 Baisakh-Old

Candidates are required to give their answers in their own words as far as practicable.
Attempt All questions.
The figures in the margin indicate Full Marks
Assume suitable data if necessary
[2+5]
• 1. What is convolution summation? Explain it with derivations and examples.
• [2+5]
• 2. Explain the properties of LTI systems with suitable examples.
• [8]
• 3. If input sequences are x[-4] = 2, x[-2] = -1, x[0] = -2 and x[1] = 3, impulse responses to the system are h[-2] = 1, h[-1] = 0.75, h[0] = 0.5 and h[1] = 0.25, calculate output sequences and plot input, impulse response and output.
• [4+8]
• 4. Given a system with complex conjugate zeros at $0.3 \pm j0.6$ and complex conjugate poles at $0.8 \pm j0.7$ and $0.3 \pm j0.8$. Draw the diagram in z-plane and magnitude response of the system.
• [7]
• 5. Explain the frequency response for the rational system function with suitable derivations.
• [7]
• 6. Compute and draw the lattice structure of given FIR filter. $$H(z) = 1 + 0.4z^{-1} + 0.6z^{-2} + 0.25z^{-3} + 0.35z^{-4}$$
• [6+2]
• 7. Define One's complement, 2's complement and sign magnitude representation of numbers. Represent 192/220 in a 8 bit 2's complement form.
• [8]
• 8. Explain about Park's McClellan's algorithm with suitable derivation and flow chart.
• [10]
• 9. Design a low pass discrete time filter by applying impulse invariance to an approximate Butterworth continuous filter, if passband frequency is $0.3\pi$ radians and maximum deviation of 1 dB below 0 dB gain in the passband. The maximum gain of -15dB and frequency is $0.4\pi$ radians in the stopband. Consider sampling frequency 0.5 Hz.
• [6]
• 10. Find the FFT of the signal x[n] = (3, 6, 5, 5, 3, 3, 6, 3).