1 (a)
Prove convolution property of Fourier Transform.
5 M
1 (b)
State and prove final value Theorem of Laplace Transform.
5 M
1 (c)
Prove shifting property of Z transform.
5 M
1 (d)
Determine energy and / or power of following signals. i) x(n)=(35)nu(n)−(4)nu(−n−1)ii) x(t)=4e−2tu(t)
5 M
2 (a)
Obtain output y(t)=x(t)*h(t) using graphical convolution.
x(t)=1+t for −1≤t≤0=1−t for 0≤t≤1 h(t)=1 for 0≤t≤2=0 elsewhere
x(t)=1+t for −1≤t≤0=1−t for 0≤t≤1 h(t)=1 for 0≤t≤2=0 elsewhere
10 M
2 (b)
Obtain h(n) for all possible ROC conditions. Also plot the ROC comments on causality and stability at the system. H(z)=4z(z2−8z+9)(z−13)(z−3)(z+4)
10 M
3 (a)
A.C.T. LTI system has d2y(t)dt2+5dy(t)dt+6y(t)=7dx(t)dt−3x(t) i) Determine Transfer function.
ii) Obtain impulse response
iii) Obtain unit Ramp response.
ii) Obtain impulse response
iii) Obtain unit Ramp response.
8 M
3 (b)
Plot the magnitude and phase spectrum of the periodic signal. Show below.
8 M
3 (c)
Obtain initial and final value: if X(z)=3z24z2+5z+1
4 M
4 (a)
If two subsystem are connected in cascade
h1(n)=(0.9)n u(n) ? 0.5(0.9)n-1 u(n-1)
h2= (0.5)n u(n) ? (0.5)n-1 u(n-1)
Determine overall impulse response of the interconnected system.
h1(n)=(0.9)n u(n) ? 0.5(0.9)n-1 u(n-1)
h2= (0.5)n u(n) ? (0.5)n-1 u(n-1)
Determine overall impulse response of the interconnected system.
8 M
4 (b)
Obtain z transform of the following signal using properties of z transform. x(n)=(34)n−1sin(π6n)u(n)
6 M
4 (c)
Prove Parsevals theorem of Fourier series.
6 M
5 (a)
Obtain circular convolution of
x1(n)= [3 2 1 4]
x2 (n) = [ 5 7 -8 2]
x1(n)= [3 2 1 4]
x2 (n) = [ 5 7 -8 2]
5 M
5 (b)
Obtain Laplace Transform of following waveforms using its properties.
i)
i)
5 M
5 (c)
Obtain zero input response, zero state response and total response of a D.T.L.T.I. system. y(n)+7y(n−1)+12y(n−2)=4 x(n)−11x(n−1)if y(−1)=1 y(−2) x(−1)=0if input x(n)=u(n)= unit step signal
10 M
6 (a)
Obtain Fourier transform of the following signal.
6 M
6 (b)
Plot even and odd parts of following signals.
6 M
6 (c)
Obtain h(t) for causal and stable system If H(s)=s2?3s+11(s−1)(s+2)(s+3) Plot the ROC and pole's and zero's of the system.
8 M
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