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. Define Energy and Power type signal with suitable example. Check the signal $ x[n] = \cos(2n\pi /5) + \sin(\pi n/3) $ is periodic or not.
- 2. Define LTI system. Find the output of LTI system having impulse response h[n] = 2u[n] - 2u[n-4] and input signal x[n] = $ (1/3)^{n}u[n] $.
- 3. State the properties of region of convergence (ROC)? Derive the time shifting property of Z-transform.
- 4. Why do we need Differential Equation? Draw Pole-Zero in Z-plane and plot magnitude response (not to scale) of the system described by the difference equation

y[n] - 0.4y[n-1] + 0.2y[n-2] = x[n] + 0.1x[n-1] + 0.06x[n-2]. - 5. Determine the Direct Form II realization of the following system.

y(n) = -0.1y(n-1) + 0.72y(n-2) + 0.7x(n) - 0.252x(n-2). - 6. Compute the lattice coefficients and draw lattice structure of the following FIR system. $$ H(z) = 1 + 2z^{-1} - 3z^{-2} + 4z^{-3} $$.
- 7. Design a digital FIR filter for the design of the low pass filter having $ w_{p} = 0.3\pi, w_{s} = 0.5\pi, \alpha_{s} = 40dB $ using suitable window function.
- 8. What is optimum filter? Describe Remez exchange algorithm for FIR filter design with flow chart.
- 9. What is the advantage of bilinear transformation? Design a low pass discrete time Butterworth filter applying bilinear transformation having specifications as follows:

Pass band frequency $ (w_{p}) = 0.25\pi radians $

Stop band frequency $ (w_{s}) = 0.55\pi radians $

Pass band ripple $ (\delta_{p}) = 0.11 $

And stop band ripple $ (\delta_{s}) = 0.21 $

Consider sampling frequency 0.5Hz

Also, convert the obtained digital low-pass filter to high-pass filter with new pass band frequency $ (w^{\prime}_{p}) = 0.45\pi $ using digital domain transformation. - 10. Why do we need FFT? Find 8-point DFT of sequence x[n] = {1, 1, 2, 2, 1, 1, 2, 1} using Decimation in frequency FFT (DIFFT) algorithm. 2+7
- 11. Find $ x_{3}[n] $ if DFT of $ x_{3}[n] $ is given by $ X_{3}(k) = X_{1}(k)X_{2}(k) $ where $ X_{1}(k) $ and $ X_{2}(k) $ are 4-point DFT of $ x_{1}[n] = {1, 2, -2} $ and $ x_{2}[n] $ = {1, 2, 3, -1} respectively.

[2+2]

[1+4]

[3+3]

[2+2+6]

[4]

[6]

[8]

[1+6]

[2+9+4]

[7]

[6]