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Discrete Time Signal Processing - Jun 18 (Old Credit Based Grading System)
Electronics And Telecomm (Semester 5)
Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.
Q1) Solve any four.
1) $H_1(z) = 6+Z^{-1} + 6Z^{-2}$
1) $H_2(z) = 1-Z^{-1} - 6Z^{-2}$
- Find linear convolution using circular convolution.
- Find circular convolution using DFT-IDFT.
$$H(s) = \frac{2}{(s+1) (s+2)} \space\space\space\space if \space T_s=1s$$
Passband attenuation = 1 dB
Stopband attenuation = 40dB
Passband edge frequency = 200 Hz
Stopband edge frequency = 540 Hz
Sampling frequency = 8 KHz
Use Bilinear transformation method.
$$ Hd(e^{j\omega}) \space\space\space\space \frac{-\pi}{4} \le w \le \frac{\pi}{4}$$
$$ = 0\space\space\space\space \frac{\pi}{4} \le w \le \pi$$
Detemine the filter coefficients $h_d(n)$ if the window function is defined as
$$ w(n) = 1 \space \space \space \space 0 \le n \le 4 $$
$$ = 0 \space \space \space \space otherwise$$
Also determine the frequency response $H(e^{j\omega})$ of the designed filter.
i) $x_1(n)$ = {4,1,2,3}
ii) $x_2(n)$ = {2,3,4,1}
iii) $x_3(n)$ = {6,4,6,4}
$y(n) = -0.1y(n-1) + 0.2y(n-2) + 3x(n) + 3.6x(n-1) + 0.6x9n-2)$
Q6) Write short notes on: