The transfer function


The transfer function


The transfer function \ H(s) of a filter is the ratio of the output signal \ Y(s) to that of the input signal \ X(s) as a function of the complex frequency \ s:
\ H(s)=\frac{Y(s)}{X(s)}
with \ s = \sigma + j \omega.
The transfer function of all linear time-invariant filters, when constructed of discrete components, will be the ratio of two polynomials in \ s, i.e. a rational function of \ s. The order of the transfer function will be the highest power of \ s encountered in either the numerator or the denominator.



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