Transforms

Starred transform

In applied mathematics, the starred transform, or star transform, is a discrete-time variation of the Laplace transform, so-named because of the asterisk or "star" in the customary notation of the sampled signals. The transform is an operator of a continuous-time function , which is transformed to a function in the following manner: where is a Dirac comb function, with period of time T. The starred transform is a convenient mathematical abstraction that represents the Laplace transform of an impulse sampled function , which is the output of an ideal sampler, whose input is a continuous function, . The starred transform is similar to the Z transform, with a simple change of variables, where the starred transform is explicitly declared in terms of the sampling period (T), while the Z transform is performed on a discrete signal and is independent of the sampling period. This makes the starred transform a de-normalized version of the one-sided Z-transform, as it restores the dependence on sampling parameter T. (Wikipedia).

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Related pages

Line integral | Residue theorem | Z-transform | Convolution theorem | Dirac comb | Laplace transform | Applied mathematics