Transfer functions can be derived for aa)nonlinear and time invariant systemb)nonlinear and time variant systemc)linear and time variant systemd)linear and time invariant systemCorrect answer is option 'D'. Can you explain this answer? - EduRev Electrical Engineering (EE) Question

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Transfer functions can be derived for a

a)
nonlinear and time invariant system
b)
nonlinear and time variant system
c)
linear and time variant system
d)
linear and time invariant system

Correct answer is option 'D'. Can you explain this answer?

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Transfer functions can be derived for aa)nonlinear and time invariant ...

Concept:

Transfer Functions are particularly useful in LTI systems for two reasons:
If your input is made up of a bunch of these little parts, then you can use the transfer function to find the combined output. For instance, if your input was sin(t)+sin(2t), then your output would be:

ysin(t) + sin(2t) = ysin(t) + ysin(2t) = 10sin(t) + 2sin(2t)

So, the transfer function tells us how the system reacts to all types of inputs. This is not true for non-linear systems, so the transfer function isn't useful there.

If your input is delayed, then the output is also delayed:

ysin(t − 1) = 10sin(t - 1)

So, the transfer function is valid for time-shifted inputs. Again, for time-variant systems, this isn't true, so if your input has phase shifts, then the transfer function is useless.

To sum up: LTI systems have nice properties that let us use a simple-looking transfer function to deal with non-simple inputs. When you take away linearity and time-invariance, the transfer function doesn't give you enough information to be helpful.

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Transfer functions can be derived for aa)nonlinear and time invariant ...

Concept:

Transfer Functions are particularly useful in LTI systems for two reasons:
If your input is made up of a bunch of these little parts, then you can use the transfer function to find the combined output. For instance, if your input was sin(t)+sin(2t), then your output would be:

ysin(t) + sin(2t) = ysin(t) + ysin(2t) = 10sin(t) + 2sin(2t)

So, the transfer function tells us how the system reacts to all types of inputs. This is not true for non-linear systems, so the transfer function isn't useful there.

If your input is delayed, then the output is also delayed:

ysin(t − 1) = 10sin(t - 1)

So, the transfer function is valid for time-shifted inputs. Again, for time-variant systems, this isn't true, so if your input has phase shifts, then the transfer function is useless.

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Transfer functions can be derived for aa)nonlinear and time invariant systemb)nonlinear and time variant systemc)linear and time variant systemd)linear and time invariant systemCorrect answer is option 'D'. Can you explain this answer?

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