STUPIDSID
Solve any four questions:-
1 (a)
State the properties of Laplace transform and derive convolution property of Laplace transform.
5 M
1 (b)
Compare energy and power signals.
5 M
1 (c)
Prove that \( \int^\infty_{-\infty}x(t)dt=o \text{ if} x(t) \text{ is odd} \)
5 M
1 (d)
Determine initial and final values of x(n) if \[ x(z) = \dfrac {z}{2z^2 ? 3z+1}|z|>1 \]
5 M
1 (e)
State and prove parseval's theorem.
5 M
2 (a)
Find trigonometric Fourier series of the following signal:
5 M
2 (b)
A system transfer function is given by \[ H(s) = \dfrac {1}{(s^2-16)(s^2-9)} \] Determien h(t) if (i) System is stable (ii) System is causal (iii) System is neither stable nor causal.
5 M
3 (a)
Perform linear convolution using circular, convolution for the following \[ x(n)=\left \{ \underset{\uparrow}{1}, 2, 3 \right \}, \ h(n)= \left \{ \underset{\uparrow}{1},1 \right \} \]
10 M
3 (b)
Determine whether the following systems are memoryless, linear causal time - variant and stable,
i) y(n)=n x(n)
ii) y(t) = (t-2) ex(t).
i) y(n)=n x(n)
ii) y(t) = (t-2) ex(t).
10 M
4 (a)
Determine whether the following signals are energy signals, power signals or neither and find values of energy and power (i) x(n)=A ejωn
(ii) x(t)=A sin wt
(ii) x(t)=A sin wt
6 M
4 (b)
Check whether the following signals are periodic or not? If periodic find its fundamental period.
i) x(n)=Cos 0.01 πn
ii) x(t)=10 sin 12 π t+4 sin 18 πt
i) x(n)=Cos 0.01 πn
ii) x(t)=10 sin 12 π t+4 sin 18 πt
4 M
4 (c)
Sketch the following signals if x(t) is given as follows:
(i) x(2t)
(ii) x (-2 +t)
(iii) x(t) δ(t)
(iv) x(t+1) u(t)
(i) x(2t)
(ii) x (-2 +t)
(iii) x(t) δ(t)
(iv) x(t+1) u(t)
10 M
5 (a)
Find the inverse Laplace transform for all possible ROCs. \[ i) \ x(s) = \dfrac {3s+7}{s^2 -2s-3} \ ii) \ x(s) = \dfrac {5s-10}{9s^2-16} \]
10 M
5 (b)
The differential equation of a system is given by
y?(t)-y?(t)-6y(t)=x(t)
Find (i) H(S) (ii) h(t) (iii) Step response of the system
y?(t)-y?(t)-6y(t)=x(t)
Find (i) H(S) (ii) h(t) (iii) Step response of the system
10 M
6 (a)
Find odd and even part of given signal r(t)=3 t3+2t2+4t+9.
4 M
6 (b)
Find the Fourier transform of signum function.
6 M
6 (c)
Find Z-inverse of the following signal \[ x(z) = \dfrac {1}{(1+z^{-1})(1-2z^{-1})^2}
10 M
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