Harmonic Analysis

TL;DR

A method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms, of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying.

Abstract

This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying. There is a connection between harmonic equations in rectangular and polar coordinate systems. The connection established here and used to create a very robust iterative algorithm for a conformal mapping calculation. There is also suggested a new ratio (and an efficient way of computing it) of two oscillative signals.

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