Matlab Fourier Analysis

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Matlab Fourier Analysis. 主講人：戴富隆. Item: Fourier Transform introduction 地震資料來源 使用指令 程式介紹. Fourier Transform introduction 傅立葉（ Fourier, Jean Baptiste Joseph, 1768-1830 ） 十九世紀法國的數學家傅立葉發現了一個定理，即：任何的訊號（例如聲音、 影像等等）均可被拆解為頻率、振幅、相位角不等之正弦波的組合。. 傅立葉級數 :. 傅立葉複數轉換對 將信號由時間領域轉換到頻率領域

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Matlab Fourier Analysis

Item:

• Fourier Transform introduction
• 地震資料來源
• 使用指令
• 程式介紹

Fourier Transform introduction

• 傅立葉（Fourier, Jean Baptiste Joseph, 1768-1830）
• 十九世紀法國的數學家傅立葉發現了一個定理，即：任何的訊號（例如聲音、 影像等等）均可被拆解為頻率、振幅、相位角不等之正弦波的組合。

F(ω) = ∫ f(x)exp(-jωx)dx

F(x) =1/(2π) ∫ F(ω)exp(jωx)dω

-∞

-∞

Discrete Fourier Transform

X(k)= ∑ X(n) exp(-j2πnk/N) , for k=0…N-1

Inverse Discrete Fourier Transform

X(n)=1/N ∑ X(k) exp(-j2πnk/N) , for n=0…N-1

N-1

n=0

N-1

K=0

FFT (Fast Fourier Transform)

Cooley and Tukey 於 1965提出FFT法

X(m)=1/N ∑ X(n)wmn , w= exp(-j2π/N)

N-1

n=0

3. 使用指令

fft:

FFT(X) is the discrete Fourier transform (DFT) of vector X. For matrices, the FFT operation is applied to each column.

angle:

returns the phase angles, in radians, of a matrix with complex elements.

phase angles = tan-1[I(f)/R(f)] , I(f)虛部 R(f)實部

angle(2+3i) = tan-1(3/2)= 0.9828

Subplot:

creat axes in titled position

SUBPLOT(m,n,p), or SUBPLOT(mnp), breaks the Figure window into an m-by-n matrix of small axes, selects the p-th axes for the current plot, and returns the axis handle.

unwrap:

unwraps radian phases P by changing absolute

jumps greater than pi to their 2*pi complement.

It unwraps along the first non-singleton dimension of P. P

can be a scalar, vector, matrix, or N-D array.

figure:

FIGURE(H) makes H the current figure,

abs:

ABS(X) is the absolute value of the elements of X.

4. 程式介紹

% StationCode: CHY080 %草嶺

% LocationLongitude(°E): 120.678

% LocationLatitude (°N): 23.597

% LocationElavation(M): 840.0

% InstrumentKind: A900A(T362002.263 )

% StartTime: 1999/ 9/20 17:47: 2.0

% SampleRate(Hz): 200

% AmplitudeUnit: gal

% RecordLength(sec): 90.0

% DataSequence: U(+); N(+); E(+)

% Data: 3F10.3

clear;

N = 18000; % SampleRate(Hz): 200 * RecordLength(sec): 90

T = 1/200; %%1/SampleRate(Hz)

k = 0:N-1;

h = k*(1/(N*T)); % hertz

ux = ch080(:,1)‘; % ch080.txt 第一行資料. ’ 轉為列

fu = fft(ux);

up = unwrap(angle(fu));

figure(1);

%畫3列圖.

% plot(0:T:T*(N-1),ux), x軸從0:T*(N-1), step T

subplot(311);plot(0:T:T*(N-1),ux),ylabel(\'Amplitude (gal)\'),xlabel(\'Time (s)\'),grid on,title(\'921-草嶺sh080-Vertical component\')

subplot(312);plot(h(1:N),abs(fu)),ylabel(\'abs(FFT[Amp]])(gal)\'),xlabel(\'Frequency (Hz)\'),grid on

n = ch080(:,2)\';

fn = fft(n);

np = unwrap(angle(fn));

figure(2);

subplot(311);plot(0:T:T*(N-1),n),ylabel(\'Amplitude (gal)\'),xlabel(\'Time (s)\'),grid on,title(\'921-草嶺sh080-NS component\')

subplot(312);plot(h(1:N),abs(fn)),ylabel(\'abs(FFT[Amp])(gal)\'),xlabel(\'Frequency (Hz)\'),grid on

e = ch080(:,3)\';

fe = fft(e);

ep = unwrap(angle(fe));

figure(3);

subplot(311);plot(0:T:T*(N-1),e),ylabel(\'Amplitude (gal)\'),xlabel(\'Time (s)\'),grid on,title(\'921-草嶺sh080-EW component\')

subplot(312);plot(h(1:N),abs(fe)),ylabel(\'abs(FFT[Amp])(gal)\'),xlabel(\'Frequency (Hz)\'),grid on