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Signals and Systems by Smarajit Ghosh

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4.11 PARTIAL FRACTION EXPANSIONS

The Laplace transformation of any function may contain the ratio of two polynomials in s-domain i.e.

 

image

 

where Q(s) is of a higher degree than P(s).

Therefore, the expansion of quotient into the sum of several fraction is required to obtain inverse transforms.

The application of partial fraction expansion method and another method popularly known as Heaviside expansion theorem is discussed here.

Equation (4.45) can be written as

 

image

 

 

  1. General Case

    Let us consider an example

     

     

    Factorizing the denominator ...

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