Coefficient-of-Determination Fourier Transform

TL;DR

This paper introduces a novel spectral analysis algorithm that uses the coefficient of determination to convert time-domain data into high-resolution spectral representations, allowing flexible resolution and reversible transformations.

Contribution

The proposed algorithm uniquely employs the coefficient of determination to achieve high-resolution spectral transforms with customizable resolution and reversibility.

Findings

Produces spectral data at any user-defined resolution.

Can transform spectral data back to the temporal domain.

Provides high-resolution spectral representations of time-series data.

Abstract

This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this algorithm is that it can produce spectral data at any user-defined resolution, and this highly resolved spectral data can be transformed back to the temporal domain.