STUPIDSID
1 (a)
Derive the Parsevel's Energy relation. State the significance of Parsevel's theorem.
5 M
1 (b)
One of zeros of a Causal Linear phase FIR filter is at 0?5 ej?/3. Show the locations of other zeros and hence find the transfer function and impulse response of the filter.
5 M
1 (c)
A two pole pass filter has the system function \[H\left(z\right)=\frac{b_0}{{\left(1-pz^{-1}\right)}^2}\] Determine the values of b0 and P. such that the frequency response H(w) satisfies the condition \[H\left(0\right)=1\ and\{\left\vert{}H\left(\frac{\pi{}}{4}\right)\right\vert{}}^2=\frac{1}{2}\]
5 M
1 (d)
Consider the signal x(n) = anu(n), |a| <1 :-
(i) Determine the spectrum.
(ii) The signal x(n) is applied to a decimator that reduces the rate by a factor 2. Determine the output spectrum.
(i) Determine the spectrum.
(ii) The signal x(n) is applied to a decimator that reduces the rate by a factor 2. Determine the output spectrum.
5 M
2 (a)
An analog signal xa(t) is band limited to the range 900 ? F ? 1100 Hz. It is used as an input to the system shown in figure. In this system, H(w) is an ideal lowpass filter with cut off frequency FC =125 Hz
(i) Determine and sketch the spectra x(n), w(n), v(n) and y(n).
(ii) Show that it is possible to obtain y(n) by sampling xa(t) with period T=4 milisecond
(i) Determine and sketch the spectra x(n), w(n), v(n) and y(n).
(ii) Show that it is possible to obtain y(n) by sampling xa(t) with period T=4 milisecond
10 M
2 (b)
Derive and draw the FFT for N = 6 = 2.3 use DITFFT method. X(n) ={ 1 2 3 1 2 3 } Find x(k) using DITFFT for N= 6=2.3
10 M
3 (a)
Design a digital Butterworth low pass filter satisfying the following specifications using bilinear transformations. (Assume T=15).
\[0.9=\left\{\begin{array}{l}\leq{}\left\vert{}H\left(e^{jw}\right)\right\vert{}\leq{}1;\\ \ \ \&0\leq{}W\leq{}\frac{\pi{}}{2} \\\leq{}\left\vert{}H\left(e^{jw}\right)\right\vert{}\leq{}0.2\ ;\ \ \\&\frac{3\pi{}}{4}\leq{}W<\pi{}\end{array}\right.\]
\[0.9=\left\{\begin{array}{l}\leq{}\left\vert{}H\left(e^{jw}\right)\right\vert{}\leq{}1;\\ \ \ \&0\leq{}W\leq{}\frac{\pi{}}{2} \\\leq{}\left\vert{}H\left(e^{jw}\right)\right\vert{}\leq{}0.2\ ;\ \ \\&\frac{3\pi{}}{4}\leq{}W<\pi{}\end{array}\right.\]
12 M
3 (b) (i)
If x(n) = { 1+5j, 2+6j, 3+7j, 4+8j }. Find DFT X(K) using DIFFFT.
4 M
3 (b) (ii)
Using the result obtained in (i) not otherwise, Find DFT of following sequences :-
x1(n) = { 1,2,3,4 } and x2(n) = {5 6 7 8 }
x1(n) = { 1,2,3,4 } and x2(n) = {5 6 7 8 }
4 M
4 (a) (i)
Obtain System Function.
4 M
4 (a) (ii)
Obtain Difference Equation.
2 M
4 (a) (iii)
Find the impulse response of system
3 M
4 (a) (iv)
Draw pole-zero plot and comment on System Stability
3 M
4 (b)
Derive the Expression for impulse invariance technique for obtaining transfer function of digital filter from analog filter. Derive the necessary equation for relationship between frequency of analog and digital filter.
8 M
5 (a)
What do you mean by inplace computations in FFT algorithm ?
4 M
5 (b)
Find number of real additions and multiplication required to find DFT for 82 point. Compare them with number of computations required if FFT algorithms is used.
4 M
5 (c)
Design a digital Chebyshev filter to satisfy the following constraints :-
\[0.707=\left\{\begin{array}{l}\leq{}\left\vert{}H\left(e^{jw}\right)\right\vert{}\leq{}1;\\ \ \ \&0\leq{}w\leq{}0.2\pi{} \\\leq{}\left\vert{}H\left(e^{jw}\right)\right\vert{}\leq{}0.1\ ;\ \ \\&0.5\leq{}w<\pi{}\end{array}\right.\]
Use bilinear transformation and assume T=1 second.
\[0.707=\left\{\begin{array}{l}\leq{}\left\vert{}H\left(e^{jw}\right)\right\vert{}\leq{}1;\\ \ \ \&0\leq{}w\leq{}0.2\pi{} \\\leq{}\left\vert{}H\left(e^{jw}\right)\right\vert{}\leq{}0.1\ ;\ \ \\&0.5\leq{}w<\pi{}\end{array}\right.\]
Use bilinear transformation and assume T=1 second.
12 M
6 (a)
Given x(n) = n+1 and N=8, find DFT X(K) using DIFFFT algorithm
8 M
6 (b)
Obatin Direct form I, Direct form II realization to second order filter given by -
y(n) = 2b cos w0y(n-1) - b2y (n-2) + x(n) - b cos w0x(n-1).
y(n) = 2b cos w0y(n-1) - b2y (n-2) + x(n) - b cos w0x(n-1).
8 M
6 (c)
Explain the concept of decimation by integer (M) and interpolation by integer factor (L).
4 M
7 (a)
Write short note on set top box for digital TV receiver.
4 M
7 (b)
Application of Signal Processing in Radar.
4 M
7 (c)
What is linear phase filter? What condition are to be satisfied by the impulse response of an FIR system in order to have a linear phase? Define phase delay and group delay.
8 M
7 (d)
Short note on Frequency Sampling realization of FIR filters.
4 M
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