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. Compute and plot even and odd component of the sequence x(n) = 2u[n] - 2u[n - 4] where u[n] is unit step sequence.
- 2. Write whether or not the following sequences are periodic and write the period.

a) $ x[n] = \cos\left(\frac{5\pi}{3}n\right) $

b) $ x[n] = \sin\left(\frac{\pi n}{\sqrt{2}} + \frac{\pi}{8}\right) $ - 3. Find the discrete Fourier coefficients of the periodic sequence with period N=11 defined over a period as $ x[n] = \begin{cases}1, & |n|\leq{2}\\0, & 2\lt{|n|}\leq{5}\end{cases} $
- 4. Show whether or not the system y(n) = nx[2(n - 2)], n > 0 is (a) linear, (b) time invariant, (c)memoryless.
- 5. Find the system function H(z) of the system characterized by difference equation $ y[n] - \frac{5}{6}y[n - 1] - \frac{1}{6}y[n - 2] - x[n] = 0. $ Find the poles and zeros of the system. Use the pole-zero diagram to plot the approximate frequency response magnitude of the system.
- 6. Realize the system function $$ H(z) = \frac{\left(1-\frac{1}{3}z^{-1}\right)\left(1-\frac{1}{4}z^{-1}\right)\left(1-\frac{1}{8}z^{-1}\right)}{\left(1-\frac{5}{6}z^{-1}\right)\left(1-\frac{1}{6}z^{-1}\right)\left(1-\frac{3}{4}e^{-j\frac{\pi}{4}}z^{-1}\right)\left(1-\frac{3}{4}e^{j\frac{\pi}{4}}z^{-1}\right)} $$ in terms of cascade of second order sections. Draw the block diagram of the cascade realization.
- 7. Show by giving examples that the quantization error by truncation for sign magnitude number, $ e_{tsm}, $ lies in the range $ -(2^{-b} - 2^{-b_{u}}) \leq e_{tsm} \leq (2^{-b} - 2^{-b_{u}}) $ and that for the 2's complement number, $ e_{t2c}, $ lies in the range $ -(2^{-b} - 2^{-b_{u}}) \leq e_{t2c} \leq 0. \space b_{u} $ is the number of bits before quantization and b is the number of bits after quantization.
- 8. How does an IIR filter differ from an FIR filter?

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