memo sice 2014/10/18 Saichi Kato Graph.K

Fourier Transform フーリエ変換

Fourier Transform フーリエ変換

X(f) =
-j2πft
x(t)e dt   (-∞ ≦ f ≦ ∞)   ・・・(1.1) FT

Revers Fourier Transform 逆フーリエ変換

x(t) =
j2πft
X(f)e df   (-∞ ≦ f ≦ ∞)   ・・・(1.2) RFT

DFT (Discrete Fourier Transfer) Furier Transform into ⊿t 有限なフーリエ変換

周波数の基本
f =
1
t
t = nt   (0≦ n ≦ N -1)
f =
kfs
⊿tN
(0≦ k ≦ N -1) ・・・ (2.1)
k: sampling rate ⊿tN: 2π(1 revolution) sampling
f =
kfs
N
(0≦ k ≦ N -1) ・・・ (2.2)

FFT (Fast Fourier Transform) 高速フーリエ変換

I have conferm, It's not correctory. 要確認。
F(x)=
N-1
- j 2πtx
N
Σ f(t)e
F(x)=
1
N
N-1
j 2πtx
N
Σ F(t)e

Series of Fourier Expansion フーリエ級数と展開式

The following is jus memo , web editions "New Fourier's adventure",. it's orignal edition's title is New Fourier's adventure . I lande FFT with this book. It's familial for me.
昔読んだ「フーリエの冒険」の Web 版を見つけたのでメモ。
新 フーリエの冒険 Visual編
f(t) = a0 +
Σ (an cos n at + bn sin n at)
a0 =
1
T
T
f(t)dt
an =
2
T
T
f(t) cos n atdt
bn =
2
T
T
f(t) sin n atdt