Fourier Analysis Terms 傅立葉分析相關名詞

Joseph Fourier (1768-1830) - French mathematician and physicist

Fourier analysis 傅立葉分析 function ---decompose---> oscillatory components
Fourier synthesis 傅立葉合成 oscillatory components ---combine--> function

Trigonometric series 三角級數 (Wikipedia)

Fourier series 傅立葉級數 => 可表示週期函數
Fourier transform 傅立葉轉換
discrete-time Fourier transform (DTFT) 離散時間傅立葉轉換
discrete Fourier transform (DFT) 離散傅立葉轉換

Fourier series:
periodic function 週期函數
f(x) = f(x + t) where t is the period

fundamental period 基本周期 t
fundamental frequency 基本頻率/基頻 f = 1/t
fundamental angular frequency 基本頻率/基頻 ω₀ = 2πf = 2π/t

fast Fourier transform (FFT) 快速傅立葉轉換

Periodic function => Fourier series
Non-periodic function => Fourier transform
Discrete function => discrete Fourier transform

periodic signal representations:
1.  sin + cos functions
2. amplitude + phase
3. complex Fourier series

Harmonic 諧波
Harmonic series 諧波列/泛音列
Overtone 泛音

analytic signal 解析訊號

Reference

Fourier analysis (Wikipedia)
Advanced Engineering Mathematics (10th edition), p474
Engineering Mathematics Exposed page 503