Fourier Integral and Fourier Transform

                  Fourier integral

Introduction 何謂譜
From Fourier series to Fourier integral(魯蛋版)(怡絹佩諭版 .nb1 .nb2)傅立葉級數與轉換(偶函數)(奇函數)(階梯函數和Delta函數)(不連續的函數微分要小心)常態分布函數與傅立葉轉換(word)(pdf)

                  Fourier transform

Fourier transform(ii)
                                                 Fourier Transform(ppt)                                             
褶積  

          Convolution(ppt file)    convolution動畫    correlation動畫   convolution&correlation   sin波*方形波(.nb/.doc/.vcr)
                                                   火車入洞                  方形波*sin波(.nb/.doc/.vcr)                                     sinsin摺積動畫

影片區(youtube)

MIT

Convolution

Fourier transform(iii)            傅立葉轉換與拉普拉斯轉換之比較
Parseval's 定理

                                                 Parseval's theorem    Proof  COVID-19遠距版

Energy  form(雅鈞) 
Some interesting properties of operators
Hilbert 轉換

                                         因果函數Fourier轉換特性

 

影片區(youtube)

Hilbert transform

 

                                                Hilbert transform 1

                                                Hilbert transform 2

                              Geometric Meaning for Fourier Transform

例題

                                      Example for Fourier Transform Fourier轉換練習

Properties of Fourier transform
Table of Fourier integral

一路走來坦蕩蕩 (word) (pdf)

Gibbs 現象

                               Gibbs phenomenon by Fourier transform (Pointwise) Uniform Convergence

Fourier transform(i)
cos & sin傅立葉轉換

                                                        cos & sin傅立葉轉換         單頻函數傅立葉轉換

集中力函數的Fourier(word)楊騰
常態分布函數與傅立葉轉換

cARSLAW-pAO(jpg)、cARSLAW-pAO-BOOK(jpg)、CHURCHILL(jpg)、OPERATIONAL-mATH2021(jpg)、由統計算工數(jpg)、常態分布函數與傅立葉轉換(doc)、與操作數學結緣四十年(doc)、遠端現學現賣解答(jpg/ppt)、操作數學的幾個有趣教學經驗談(doc)、機率密度分布函數fourier transform(jpg/ppt)、機率密度函數的三個矩(jpg/doc)

由統計算工數

                  建議叢書區

書名 作者 出版社 年代
Fourier Analysis and Its Applications Anders Vretblad Springer-Verlag 2005

 

Introduction 何謂譜

Fourier transform(iii)

From Fourier series to Fourier integral(魯蛋版)

Parseval's theorem

Fourier transform(i)

Some interesting properties of operators

Fourier transform(ii)

Comparison of Laplace Transform and Fourier Transform

Table of Fourier integral

 

因果函數Fourier轉換特性

Gibbs phenomenon by Fourier transform

Hilbert transform 1

Properties of Fourier transform

Hilbert transform 2
Example for Fourier transform (ppt) Geometric Meaning for Fourier Transform
Convolution (ppt file) Convolution (ppt 更新) convolution動畫 correlation動畫 Correlation的證明