Nature

Implementation of quantum and classical discrete fractional Fourier transforms

Two hundred years ago, Joseph Fourier introduced a major concept in mathematics, the so-called Fourier transform (FT). It was not until 1965, when Cooley and Tukey developed the ‘fast Fourier ...
IEEE

The ROCOF-DFT: A Discrete Fourier Transform Kernel Adaptation for ROCOF Tracking

With the increasing penetration of renewable resources in modern power systems, the estimation of the Rate of Change of Frequency (ROCOF) has become a critical but challenging task. Conventional ...
IEEE

Fourier Transform Evolution from DFT to FFT to QFT: the Journey of Cost Reduction from $O\left(N^{2}\right)$ to $O(N \log N)$ to $O\left(\log ^{2} N\right)$

Abstract: Paper provides description of methods for Discrete Fourier Transform computation from direct $O\left(N^{2}\right)$ approach to its $O(N \log N)$ evaluation ...
Popular Mechanics

Fourier Transforms: The Math That Made Color TV Possible

A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its ...