STUPIDSID
1 (a)
Periodic analog signal will always remain periodic when converted into digital signal. Is it true or false ? Justify your answer.
5 M
1 (b)
Frequency domain representation of a periodic discrete time signal is a periodic. Is it true or false ? Justify your answer.
5 M
1 (c)
Obtain the pole-zero plot of a causal symmetrical linear phase FIR filter with odd number of coefficients, assuming smallest length, if it is Known to have zeros at z=j, z=1, z= -1.
5 M
1 (d)
A high pass linear phase FIR filter has a magnitude response -
|H(ejw)| = 4 sin(aw) -3 sin(bw)
Find values of 'a' and 'b' assuming minimum value of N. Obtain corresponding impulse response.
|H(ejw)| = 4 sin(aw) -3 sin(bw)
Find values of 'a' and 'b' assuming minimum value of N. Obtain corresponding impulse response.
5 M
2 (a)
Classify the following (i.e. (A),(B) and (C) ) as -
(i) Linear phase/ Non- Linear phase
(ii) FIR/IIR
(iii) All pass/high pass /low pass/band pass
(iv) stable/Unstable- -
\[\left(A\right)\ \ H\left(e^{jw}\right)=3\ e^{-2jw}\]
\[\left(B\right)\ H\left(z\right)=\frac{z+0.6}{z-0.8}\]
(C) Given following pole-zero plot.
(i) Linear phase/ Non- Linear phase
(ii) FIR/IIR
(iii) All pass/high pass /low pass/band pass
(iv) stable/Unstable- -
\[\left(A\right)\ \ H\left(e^{jw}\right)=3\ e^{-2jw}\]
\[\left(B\right)\ H\left(z\right)=\frac{z+0.6}{z-0.8}\]
(C) Given following pole-zero plot.
12 M
2 (b)
Determine the zero of the following FIR systems and indicate whether the system is minimum phase, maximum phase or mixed phase
\[\left(i\right)\ H\left(z\right)=6+z^{-1}+z^{-2}\]
\[\left(ii\right)\ H\left(z\right)=1-z^{-1}-6z^{-2}\]
\[\left(iii\right)\ H\left(z\right)=1-\frac{5}{2}z^{-1}-\frac{3}{2}z^{-2}\]
\[\left(iv\right)\ H\left(z\right)=1-\frac{5}{6}z^{-1}-\frac{1}{3}z^{-2}\]
\[\left(i\right)\ H\left(z\right)=6+z^{-1}+z^{-2}\]
\[\left(ii\right)\ H\left(z\right)=1-z^{-1}-6z^{-2}\]
\[\left(iii\right)\ H\left(z\right)=1-\frac{5}{2}z^{-1}-\frac{3}{2}z^{-2}\]
\[\left(iv\right)\ H\left(z\right)=1-\frac{5}{6}z^{-1}-\frac{1}{3}z^{-2}\]
8 M
3 (a)
Design a causal digital high pass filter using windowing technique to meet the following specification:
Passband edge : 9.5 kHz
Stopband edge : 2kHz
Stopband attenuation : ?40dB
Sampling frequency : 25kHz
Passband edge : 9.5 kHz
Stopband edge : 2kHz
Stopband attenuation : ?40dB
Sampling frequency : 25kHz
10 M
3 (b)
Obtain the analog transfer function of a Butterworth low pass filter with following specification :-
Passband edge (?p) = 250 rad/sec
Passband attenuation ?0.1 dB
Stopband edge (?s) = 2000 rad/sec.
Stopband attenuation ? 60 dB
Passband edge (?p) = 250 rad/sec
Passband attenuation ?0.1 dB
Stopband edge (?s) = 2000 rad/sec.
Stopband attenuation ? 60 dB
10 M
4 (a) (ii)
Using the result obtained in (i) above and not otherwise, find DFT of following sequence :
x1(n) = { 1,3,5,7 } and
x2(n) = { 2,4,6,8 }
x1(n) = { 1,3,5,7 } and
x2(n) = { 2,4,6,8 }
5 M
4 (a)(i)
If x(n) = { 1+2j, 3+4j, 5+6j, 7+8j }. Find DFT X(k) using DIFFFT.
5 M
4 (b)
Obtain direct from I, direct from II realization to second order filter given by -
y(n) = 2 b cos(w0) y(n-1) - b2 y(n-2) + x(n) - b cos(w0) x(n-1)
y(n) = 2 b cos(w0) y(n-1) - b2 y(n-2) + x(n) - b cos(w0) x(n-1)
10 M
5 (a)
Using linear convolution find y(n) for the sequence --
x(n) = { 1,2,-1,2,3,-2,-3,-1,1,2,-1 } and h(n) = { 1,2 }
Compare the result by solving the problem using overlap and add method.
x(n) = { 1,2,-1,2,3,-2,-3,-1,1,2,-1 } and h(n) = { 1,2 }
Compare the result by solving the problem using overlap and add method.
10 M
5 (b)
Find the response of the difference equation given by --
y(n) = 5y(n-1) - 6y(n-z) + x(n) for x(n) = u(n).
y(n) = 5y(n-1) - 6y(n-z) + x(n) for x(n) = u(n).
10 M
6 (a)
Explain up sampling by an integer factor with neat diagram and waveforms.
10 M
6 (b)
Why is the direct form FIR structure for a multirate system inefficient? Explain with neat diagrams how this inefficiency is overcome in implementing a decimator and an interpolator.
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)
Comparison of FIR and IIR filters
5 M
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