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. Find the even and odd part of signal x[n], $$ x[n] = \begin{cases}1 & for \space -4\leq n \leq 0\\2 & for \space 1\leq n\le4\end{cases} $$.
- 2. Illustrate the significance of convolution summation in digital signal analysis. Compute the convolution of the following signals: h(n) = {1, 0, 1} and x(n) = {1, -2, -2, 3, 4}.
- 3. Define Region of Convergence. Find inverse Z-transform of $ X(z) = z/{\left\{(z-1)(z-2)^{2}\right\}}, \space ROC:|Z|<1 $.
- 4. Given H(z) for a system with the following difference equation:

y(n) = x(n) + x(n-2)

Plot its poles and zeros in Z plane. Determine its magnitude response. Also, determine whether system is causal or stable. - 5. Draw lattice structure for given pole-zero system $$ H(z) = (0.5 + 2z^{-1} + 0.6z^{-2})/(1-0.3z^{-1} + 0.4z^{-2}) $$.
- 6. What do you mean by Limit Cycle? How it occurs in recursive system?
- 7. What is the condition satisfied by Linear Phase FIR filter? Show that the filter with h(n) = {-1, 0, 1} is a linear phase filter.
- 8. Use Hanning window method to design low-pass FIR filter with pass-band edge frequency $ (w_{p}) = 0.25\pi $, stop-band edge frequency $ (w_{s}) = 0.35\pi $ where main lobe width of Hanning window is $ 8\pi/M $, M is the filter length.
- 9. Why Spectral Transformation if required?
- 10. Design a low pass digital filter by impulse invariance method to an approximate Butterworth filter, if passband edge frequency is $ 0.2\pi $ radians and maximum deviation of 0.5 dB below 0 dB gain in the passband. The maximum gain of -15 dB and frequency is $ 0.35\pi $ radian in stopband, consider sampling frequency 1 Hz.
- 11. Why do we need Discrete Fourier Transform (DFT) although we have Discrete-time Fourier Transform (DTFT)? Find circular convolution between

x[n] = {1, 2} and y[n] = u[n] - u[n-4]. - 12. How fast is FFT? Draw the butterfly diagram and compute the value of x(7) using 8 pt DIT-FFT for the following sequences:

x(n) = {1, 0, 0, 0, 0, 0, 0, 0}

[3]

[2+4]

[1+5]

[2+6+2]

[6]

[1+3]

[2+4]

[9]

[2]

[13]

[2+5]

[2+6]