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Harmonic Analysis

Vladimir I Clue

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.

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.
Paper Structure (10 sections, 24 equations, 8 figures)

This paper contains 10 sections, 24 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Transform the AFC by Circulant Matrix
  3. Evaluating Analytical Functions.
  4. Obtaining values of harmonically conjugated function.
  5. Connection between harmonic equations in rectangular and polar coordinate systems
  6. Conformal Mapping
  7. Harmonic Covariation, Correlation
  8. Harmonic Covariation
  9. Harmonic Correlation
  10. References

Figures (8)

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  • ...and 3 more figures