Abstract
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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References
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Litovski, V. (2019). Transfer Function and Frequency and Time Domain Response. In: Electronic Filters. Lecture Notes in Electrical Engineering, vol 596. Springer, Singapore. https://doi.org/10.1007/978-981-32-9852-1_3
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DOI: https://doi.org/10.1007/978-981-32-9852-1_3
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