Adaptation of Fourier transform for reproducing non-periodic signals

Abstract

The Fast Fourier Transform (FFT) is a widely used algorithm for spectral analysis and signal
processing. However, the FFT is limited to analyzing periodic signals and is not suitable for nonperiodic signals. In recent years, various techniques have been developed to address this
limitation and improve the accuracy of non-periodic function approximation. In this article, we
review the limitations of using the FFT for non-periodic function approximation and discuss potential future directions for improvement. We first provide a brief overview of the FFT and its
limitations before exploring alternative methods, such as the windowed Fourier transform, the
short-time Fourier transform, and machine learning-based methods for function approximation.
We also discuss potential future directions for improvement, including the use of hybrid methods
that combine the FFT with other techniques, such as wavelet transforms or machine learningbased approaches. Finally, we discuss the implications of these developments for future research
and applications. Our review provides insights into the limitations of the FFT for non-periodic
function approximation and highlights the potential for alternative methods, such as Genetic
Algorithms (GA), to overcome these limitations and improve the accuracy of function
approximation.