Coefficient-of-Determination Fourier Transform

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.