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 ∫∞−∞x(t)dt=o ifx(t) is odd
5 M
1 (d)
Determine initial and final values of x(n) if x(z)=z2z2?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)=1(s2−16)(s2−9) 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)={1↑,2,3}, h(n)={1↑,1}
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)=3s+7s2−2s−3 ii) x(s)=5s−109s2−16
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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