### Digital Signal Analysis and Processing, 2068 Bhadra - Old questions

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

### Digital Signal Analysis and Processing, 2068 Bhadra

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
[5]
• 1. Find the energy and power of the signal x[n] = u[n].
• [6]
• 2. Find the period of the signal $x[n] = \sum_{m=-\infty}^{\infty}\delta [n-2-3m].$ Find the Fourier series coefficients of the signal x[n].
• [5]
• 3. State whether or not the system $y[n] = e^{x[2n]}$ is (a) linear (b) time invariant (c) memoryless (d) causal. Where x[n] is input to the system and y[n] is output of system.
• [5]
• 4. Convolve the sequence $x[n] = 3^{n}u[-n-5]$ and y[n] = u[n-5].
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• 5. Find the frequency response of the linear time invariant system characterized by difference equation $y[n] - \frac{10}{24}y[n-1] + \frac{1}{24}y[n-2] = x[n].$ If the input the system is $x[n] = \sin\left(\frac{\pi}{3}n\right) + \sin\left(\frac{\pi}{5}n\right)$ then determine output y[n] of the system.
• [9]
• 6. Realize the overall system function: $$H(z) = \frac{(1-\frac{1}{5}e^{-j\frac{\pi}{5}}z^{-1})(1-\frac{1}{3}z^{-1})(1-\frac{1}{5}e^{j\frac{\pi}{5}}z^{-1})}{(1-\frac{4}{5}z^{-1})(1-\frac{1}{7}e^{j\frac{\pi}{7}}z^{-1})(1-\frac{1}{5}z^{-1})(1-\frac{1}{7}e^{-j\frac{\pi}{7}}z^{-1})}$$ In terms of direct form I and direct form II structures. Draw the corresponding block diagrams of direct form I and direct form II structures.
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• 7. How the spectrum of continuous time signal is related to spectrum of corresponding discrete time signal obtained by sampling the continuous time signal? Explain. Discuss what is aliasing and how it occurs.
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• 8. If passband edge frequency $w_{p} = 0.25\pi,$ stopband edge frequency $w_{s} = 0.45\pi,$ passband ripple $\delta_{p} = 0.17$ and stopband ripple $\delta_{s} = 0.27$ then design a digital lowpass Butterworth filter using bilinear transformation technique.
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• 9. Use Blackman window method to design a low-pass FIR filter with passband edge frequency $w_{p} = 0.24\pi,$ stopband edge frequency $w_{s} = 0.34\pi$ where main lobe width of Blackman window is $\frac{12\pi}{M},$ M is filter length.
• [8]
• 10. Use the Fast Fourier Transform decimation in frequency algorithm to find the discrete Fourier Transform of the sequence x[n] = [1, -2, 2, 1].