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】高速Fourier変換(1)，FFT, Fast Fourier Transform, N=4の場合 ...

この高速フーリエ変換という名前は分かりにくいと私は思っている． この名称は，新しいフーリエ変換の形式かと誤解させる節がある． 離散フーリエ変換の高速化アルゴリズムであるだけなのに． まずは，最も簡単な$${N=2}$$の場合にどのようにDFTが計算さ ...
IEEE

Scaling the discrete Fourier transform gate in the quantum frequency processor

Abstract: We show that the d-dimensional discrete Fourier transform can be implemented by adding RF harmonics to the applied modulation in a quantum frequency processor. Implementing the d = 3 case ...
GitHub

discrete-fourier-transform

Welcome to the GPU-FFT-Optimization repository! We present cutting-edge algorithms and implementations for optimizing the Fast Fourier Transform (FFT) on Graphics Processing Units (GPUs).
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" ...
IEEE

Determination of Envelopes of Real Finite Discrete Signals Based on Discrete Fourier ...

Abstract: In numerous scientific disciplines, the advancement of digital Fourier processing-its theory, methods, and algorithms-is pivotal in addressing a spectrum of theoretical and practical ...