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Transfer Functions
We now summarize our definition of a transfer function.
- Transfer Function of a Continuous Time LTI System:
- A complex valued function
of a complex variable 
, along with a region of convergence. For belonging
to the region of convergence, the transfer function tells us what the response is to the
input signal 
, namely the response is 
.
- Transfer Function of a Discrete Time LTI System:
- A complex valued function
of a complex variable 
, along with a region of convergence. For belonging
to the region of convergence, the transfer function tells us what the response is to the
input signal 
, namely the response is 
.
Since essentially arbitrary signals can be expressed as superpositions of complex exponentials, we can use superposition and knowledge of the transfer function to determine the response to an arbitrary input signal. Thus, a transfer function completely specifies an LTI system.
R. L. Cruz
Fri Dec 25 20:53:17 PST 1998