Fair and Square Computation of Inverse -Transforms of Rational Functions
نویسندگان
چکیده
All methods presented in textbooks for computing inverse -transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence whose -transform is ; 2) computation using the inversion integral method becomes labored when has poles at the origin of the complex plane; 3) the partial-fraction expansion method, in spite of being acknowledged as the simplest and easiest one to compute the inverse -transform and being widely used in textbooks, lacks a standard procedure like its inverse Laplace transform counterpart. This paper addresses all the difficulties of the existing methods for computing inverse -transforms of rational functions, presents an easy and straightforward way to overcome the limitation of the inversion integral method when has poles at the origin, and derives five expressions for the pairs of time-domain sequences and corresponding -transforms that are actually needed in the computation of inverse -transform using partial-fraction expansion.
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