note

【信号処理】離散フーリエ変換対：DFT, Discrete Fourier Transform

すでに行った，離散フーリエ級数，DFSとほぼ同じです． 信号の周期性の仮定をしていましたが，サンプリングされた信号では， 1周期分のサンプリングとみなせば，有限長データも同じです． 復習：フーリエ変換対 信号 $${x(t)}$$ の周期性に関して，無限長 ...
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 ...
note

【信号処理】離散フーリエ級数：DFS, Discrete Fourier Series

今回は，周期信号に対する複素フーリエ級数展開（三角多項式）を離散化しよう． これで，離散フーリエ級数（DFS: Discrete Fourier Series）を得られる． まず，周期信号 $${x(t) = x(t+T)}$$ に関する離散化を行う． 周期 $${T}$$ を ${N}$ 分割しよう： T = \sum_{n=0}^{N-1} ...
IEEE

Evolution of Forward and Inverse Discrete Fourier Transform

Abstract: The problems of the evolution of the forward and inverse discrete Fourier transform are investigated. Forward and inverse discrete Fourier transform is the basis of the classical discrete ...
IEEE

Real Time Method and Algorithms for Fast Discrete Fourier Transform of Discrete Finite Signals

Abstract: The paper is devoted to the development of methods and algorithms for fast discrete Fourier transform of discrete finite signals in real time. The paper considers the case when the duration ...
GitHub

Low-Level Discrete Fourier Analysis Pipeline

The goal of this project is to demystify the Discrete Fourier Transform (DFT) by implementing it from scratch using a fundamental Linear Algebra approach, rather than relying on optimized "black box" ...
GitHub

discrete-time-fourier-transform

Add a description, image, and links to the discrete-time-fourier-transform topic page so that developers can more easily learn about it.