Question
Download Solution PDFWhich of the following transfer functions is obtained from a certain system e-4t for wait impulse response?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
A transfer function is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.
For unit impulse input i.e. r(t) = δ(t)
⇒ R(s) = δ(s) = 1
Now transfer function = C(s)
Therefore, the transfer function is also known as the impulse response of the system.
Transfer function = L[IR]
Calculation:
Impulse response = e-4t
By applying the Laplace transform, we get
Transfer function
Additional Information
Some common Laplace transforms are:
|
f(t) |
F(s) |
ROC |
|
δ (t) |
1 |
All s |
|
u(t) |
|
Re (s) > 0 |
|
t |
Re (s) > 0 |
|
|
tn |
Re (s) > 0 |
|
|
e-at |
Re (s) > -a |
|
|
t e-at |
Re (s) > -a |
|
|
tn e-at |
Re (s) > -a |
|
|
Sin at |
Re (s) > 0 |
|
|
Cos at |
Re (s) > 0 |
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