Signals and Systems

Appendix E

Partial Fraction Expansion

The technique of partial fraction expansion is very useful in the study of signals and systems, particularly in finding the time-domain signals that correspond to inverse Laplace transforms and inverse z-transforms of rational functions, that is, a ratio of two polynomials. It is based on the idea of writing a rational function, say of s or z, as a linear combination of simpler rational functions the inverse transforms of which can be easily determined. Since both the Laplace transform and the z-transform are linear transforms, writing the rational function X (z) or X (z) as a linear combination of simpler functions and finding the inverse transform of each of those simpler functions allows us to construct ...