Consider the function f(t) having Laplace transform,the final value of f(t) would be
L^{1}[F(S)] = sin ω_{0}t
f(t)  sin ω_{0}t
So,  1 < f(∞) <1
The transfer function H(S) of a stable system is
the impulse response is
System is stable
⇒
If L[f(t)] = then f(0^{+}) and f(∞) are given by
Find the laplace transform of time function shown in figure.
Taking laplace,
Consider the following signal:
the laplace transform of above system is
Consider a signal x(t) having laplace transform given by,
The time domain signal x(t) is equal to
Given that:
then, L[h(t)] is
Convolution in time domain is multiplication in sdomain.
∴
A causal LTI system is described by the difference equation, 2y[n] = αy[n 2]  2x[n] + βx[n  1]. The system is stable only if,
Taking ztransform
For system to bs stable, β can be of any value.
⇒
For system to be stable all poles should be inside unity circle.
Match ListI (Function in time domain) with ListII (Corresponding Laplace Transform F(S)) and select the correct answer using the codes given below the lists:
ListI
A.
B.
C.
D.
ListII
1.
2.
3.
4.
Codes:
The lapiace transform of
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