STUPIDSID
1 (a)
Prove differentiation property of Z.Transform.
4 M
1 (b)
Check if the system is Linear and time invariant,
i) y(t)=t2x(t)+3
ii) y(n)=x(-n)+3x(n+1)
i) y(t)=t2x(t)+3
ii) y(n)=x(-n)+3x(n+1)
4 M
1 (c)
Prove Time shift property of Laplace Transform.
4 M
1 (d)
Determine energy or power of the following signals.
i) x(t)=5u (t)
ii) x(n)=10 n u (n).
i) x(t)=5u (t)
ii) x(n)=10 n u (n).
4 M
1 (e)
State Initial and final value Theorem of Z.Transform and Laplace Transform.
4 M
2 (a)
Determine h(n) for all possible ROC condition. \[ H(z) = \dfrac {z(z^2-3z+11)}{\left ( z - \frac {1}{4} \right ) (z-4)(z+6)}\] plot all the ROC's, pole and zeros also comment on stability at the system.
10 M
2 (b)
Obtain even and odd parts of the signal
Also obtain and plot: \[ i) x_{even} (2t-1) \\ ii) \ x_{odd} \left ( \dfrac {t}{2} +1 \right ) \]
5 M
2 (c)
Determine Fourier transformation of a signum signal.
5 M
3 (a)
Obtain Fourier series of the following signal.
8 M
3 (b)
Obtain Linear convolution of
\[ x(n)= 3?(n+3) + 2?(n+1) + ?(n)- ?(n-1)
h(n)= 2?(n+2)-3?(n) + 2?(n-1) + 4? (n-2).
\[ x(n)= 3?(n+3) + 2?(n+1) + ?(n)- ?(n-1)
h(n)= 2?(n+2)-3?(n) + 2?(n-1) + 4? (n-2).
6 M
3 (c)
Obtain Fourier transform of a rectangular pulse.
6 M
4 (a)
ADT.LTI system is specified by
y(n)=-7y(n-1)-12y(n-2)+4x(n-1)-2x(n)
y(-1)=-2y(-2)=3
Determine
a) Zero input response
b) Zero state response if x(n)=(6)nu(n)
c) Total response of the system.
y(n)=-7y(n-1)-12y(n-2)+4x(n-1)-2x(n)
y(-1)=-2y(-2)=3
Determine
a) Zero input response
b) Zero state response if x(n)=(6)nu(n)
c) Total response of the system.
10 M
4 (b)
Obtain y(t)=x(t)*h(t) using graphical convolution.
10 M
5 (a)
Obtain output response of a third order C.T. LTI non-relaxed system. \[
\dfrac {d^3 y(t)}{dt^3}+ \dfrac {8 d^2 y(t)}{dt^2}+ \dfrac {17 dy (t)}{dt} + 10 y (t) = \dfrac {d^2 x(t)}{dt^2} - \dfrac {3dx (t)}{dt} + 7 x(t) \] if y(0)=-0.5
y'(0)=2
y''(0)=-1
y'(0)=2
y''(0)=-1
10 M
5 (b)
Determine Z.Transform of x(n)=(a)n sin[Ω0n] u(n) using properties of Z.T.
5 M
5 (c)
Obtain auto-correlation of x1(t)=4e-3t u(t).
5 M
6 (a)
Obtain overall impulse response signal of the interconnected system.
6 M
6 (b)
Obtain Laplace Transform of
i) x(t)=e-9tu(t)+e+6t u(-t)
ii) x(t)=(t-1) u (t-2) + tu (t)
i) x(t)=e-9tu(t)+e+6t u(-t)
ii) x(t)=(t-1) u (t-2) + tu (t)
6 M
6 (c)
Prove Parsavel's Theorem of Fourier Transform and Fourier Series.
8 M
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