A New Look at an Old Tool-the Cumulative Spectral Power of Fast-Fourier Transform Analysis

TL;DR

This paper introduces the Cumulative Spectral Power (CSP) as an innovative approach to enhance FFT analysis, addressing limitations of traditional Power Spectral Density in noisy, time-varying signals across various fields.

Contribution

The authors propose CSP as a novel method to improve FFT analysis, offering better insights into time-varying signals compared to traditional PSD.

Findings

CSP provides clearer insights in noisy, time-varying signals.

CSP demonstrates versatility across different application fields.

CSP overcomes some limitations of traditional PSD analysis.

Abstract

As an old and widely used tool, it is still possible to find new insights and applications from Fast Fourier Transform (FFT)-based analyses. The FFT is frequently used to generate the Power Spectral Density (PSD) function, by squaring the spectral components that have been corrected for influence from the instrument that generated the data. Although better than a raw-data spectrum, by removing influence of the instrument transfer function, the PSD is still of limited value for time varying signals with noise, due to the very nature of the Fourier transform. The authors present here another way to treat the FFT data, namely the Cumulative Spectral Power (CSP), as a promising means to overcome some of these limitations. As will be seen from the examples provided, the CSP holds promise in a variety of different fields.