Shift and scale invariant preprocessor.

Abstract

A preprocessor is designed to extract a set of features that enhance natural clustering by removing extraneous information. The design rerroves time shift and scale dependence by taking advantage of invariant properties of a Fourier transform followed by a Mellin transform. The preprocessor is realized using an FFT and a Mellin transform with a conventional error correction term. The error term proves to be indeterminate, but the error's bound is identified as the envelope for Mellin correction terms. Properties of the Mellin transform are employed to modify the signal so that the error correcting is no longer required. The resulting algorithms are tested with variously scaled inputs for which closed form solutions are known. With a verified modification in place, the preprocessor produces features that are invariant to shifting and scaling, while retaining enough information to classify canonic shapes, A method of improving performance is introduced.