STUPIDSID
1 (a)
Obtain a digital filter transfer function H(ω) by applying inputs invariance transformation on the analog TF.
\[H_a\left(s\right)=\frac{s}{s^2+3s+2}\] Use fs=1 K samples/sec.
\[H_a\left(s\right)=\frac{s}{s^2+3s+2}\] Use fs=1 K samples/sec.
5 M
1 (b)
Consider a filter with TF: H(z)= (z-1-a)/(1-a z-1) Identify the type of filter and justify it.
5 M
1 (c)
Find the number of complex multiplication and complex additions required to find DFT for 32 point sequence. Compare them with the number of computations required if FFT algorithm is used.
5 M
1 (d)
Consider the sequence x(n)= δ(n)+2δ(n-2) + δ(n-3). Find DFT of x(n).
5 M
2 (a)
A sequence is given as x(n)= {1+2j, 1+3j, 2+4j, 2+2j}
(i) Find X(k) using DIT-FFT algorithm.
(ii) Using the result in (i) and not otherwise find DFT of p(n) and q(n) where
p(n)={1,1,2,2}
q(n)={2,3,4,2}
(i) Find X(k) using DIT-FFT algorithm.
(ii) Using the result in (i) and not otherwise find DFT of p(n) and q(n) where
p(n)={1,1,2,2}
q(n)={2,3,4,2}
6 M
2 (b)
X(k)= {36, -4+j9.656, -4+j4, -4+j 1.656, -4, -4-j 1.656, -4 -j4, -4-j9.656} Find x(n) using IFFT algorithm (use DIT IFFT).
10 M
2 (c)
Explain the properties of symmetricity and periodicity of phase factor.
4 M
3 (a)
By means of FFT-IFFT method (DIT algo) compute Circular convolution of x(n)={2,1,2,1} h(n) = { 1,2,3,4}
8 M
3 (b)
An 8 point sequence x(n) = {1,2,3,4,5,6,7,8}
(i) Find X(K) using DIF FFT algorithm.
(ii) Let x1(n) = {5,6,7,8,1,2,3,4} Using appropriate DFT property and answer of previous part, determine X1(K).
(iii) Again use DFT property and find X2(K) where x2 (n) =x(n)+x1(n).
(i) Find X(K) using DIF FFT algorithm.
(ii) Let x1(n) = {5,6,7,8,1,2,3,4} Using appropriate DFT property and answer of previous part, determine X1(K).
(iii) Again use DFT property and find X2(K) where x2 (n) =x(n)+x1(n).
12 M
4 (a)
Draw the Lattice filter realization for the all pole filter
\[ H\left(z\right)=\frac{1}{1+\frac{3}{4}z^{-1}+\ \frac{1}{2}z^{-2}+\frac{1}{4}z^{-3}}\]
\[ H\left(z\right)=\frac{1}{1+\frac{3}{4}z^{-1}+\ \frac{1}{2}z^{-2}+\frac{1}{4}z^{-3}}\]
10 M
4 (b)
Obtain DF-I , DF-II, cascade (first order sections) and parallel (first order sections) Structures for the system described by
y(n) =-0.1 y(n-1) + 0.72 y(n-2) + 0.7 x(n) - 0.252 x(n-1).
y(n) =-0.1 y(n-1) + 0.72 y(n-2) + 0.7 x(n) - 0.252 x(n-1).
10 M
5 (a)
Design a FIR low pass digital filter using hamming window for N=7
\[ \begin {align*} H_d(e^{j\omega})&= e^{- \ 3j\omega} \ &0.75\pi \le \omega\le0.75 \pi \\ &=0 \ &0.75\pi\le|\omega|\le\pi \end {align*} \]
\[ \begin {align*} H_d(e^{j\omega})&= e^{- \ 3j\omega} \ &0.75\pi \le \omega\le0.75 \pi \\ &=0 \ &0.75\pi\le|\omega|\le\pi \end {align*} \]
10 M
5 (b)
A LPF has following specification :-
\[ \begin {align*} &0.8\le|H(\omega|\le 1 \ &for\ 0\le \omega \le0.2\pi\\ &|H(\omega|\le 0.2 \ &for \ 0.6 \pi \le \omega \le \pi \end {align*} \]
Find filter order and analog cut off frequency if
(i) Bilinear transformation is used for designing.
(ii) Impulse invariance for designing.
\[ \begin {align*} &0.8\le|H(\omega|\le 1 \ &for\ 0\le \omega \le0.2\pi\\ &|H(\omega|\le 0.2 \ &for \ 0.6 \pi \le \omega \le \pi \end {align*} \]
Find filter order and analog cut off frequency if
(i) Bilinear transformation is used for designing.
(ii) Impulse invariance for designing.
10 M
6 (a)
Explain up sampling by an integer factor with neat diagram and waveforms.
10 M
6 (b)
Explain the need of a low pass filter with a decimator and mathematically prove that ωy = ωxD.
10 M
Write notes on any four
7 (a)
Frequency sampling realization of FIR filters
5 M
7 (b)
Goertzel algorithm
5 M
7 (c)
Set top box for digital TV reception
5 M
7 (d)
Adaptive echo cancellation
5 M
7 (e)
Filter bank
5 M
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