TRIBHUVAN UNIVERSITY

INSTITUTE OF ENGINEERING

Examination Control Division

INSTITUTE OF ENGINEERING

Examination Control Division

- Full Marks:
- 80
- Pass Marks
- 30
- Time
- 3 hrs.

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

Attempt All questions.

The figures in the margin indicate Full Marks

Assume suitable data if necessary

- 1. Plot the sequence x[n] = u[n + 8] + u[n - 4].
- 2. What is the period of following signals?

(a) $$ x[n] = \cos(\frac{11\pi}{3}n) $$

(b) $$ x[n] = e^{j\frac{7}{5}n} $$ - 3. What is a sampling? How are the spectrum of continuous time signal and spectrum of signal obtained by sampling the continuous time signal related? Illustrate with diagram.
- 4. Write about the following properties of discrete time system:

[a] linearity, [b] time invariance, [c] memory, [d] causality, [e] stability - 5. Find the frequency response $ H(e^{jw}) $ of the system characterized by the difference equation y[n] - 0.8y[n - 1] + 0.15y[n - 2] - x[n] = 0. Plot the frequency response of the system.
- 6. Realize the system function

$$ \frac{1}{(1-0.5z^{-1})(1-0.7e^{-j\frac{\pi}{4}}z^{-1})(1-0.7e^{j\frac{\pi}{4}}z^{-1})(1-0.3z^{-1})} $$

in terms of cascade of second order sections. Draw the block diagram of the cascade realization. - 7. Write about the sign magnitude and 2's complement representation of binary fractional number. Write about truncation error and rounding error.
- 8. Describe digital Butterworth filter design using impulse invariance technique. What are the limitations of impulse invariance technique?
- 9. Derive the expression for frequency response of symmetric linear phase filter of length M, where M is odd.
- 10. Using the Hanning window to design a digital low-pass FIR filter with Pass band frequency $ (w_{p}) = 0.25\pi $ and Stop band frequency $ (w_{s}) = 0.3\pi. $
- 11. Perform circular convolution of the sequences x[n] = [1 0 1] and h[n] = [1 0 2 1].
- 12. Write about multiplication and convolution property of Discrete Fourier Transform.
- 11. Draw the flow diagram of four point decimation in time Fast Fourier Transform algorithm

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