Transfer Function and Frequency and Time Domain Response
It is a custom for the filtering function to be expressed in the frequency domain as a rational function of polynomials of s, the complex frequency variable. Since the natural signals are found in the time domain, the so called Laplace Transform is used to create a representation in the complex frequency domain (from now on: in the s-domain). That allows for the differential equations representing the system to be transformed into algebraic ones and consequently to extract the so called transfer functions which are their s-domain substitute.
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