MATLAB Fourier Transform

Note finished code Under construction.

clc
clear
M=100;
x0=0;
x00=1;
dx=(x00-x0)/M;
x(1)=x0;
k=1;
for ii=1:M;
    x(ii+1)=x(ii)+dx;
    f(ii)=1;
end
% eix=cosx-isinx
for ii=2:2:M-1;
    F(ii)=f(ii)*(cos(x(ii)*k*2*pi)-i*sin(x(ii)*k*2*pi));
    F(ii+1)=f(ii+1)*(cos(x(ii+1)*k*2*pi)-i*sin(x(ii+1)*k*2*pi))
 FF(ii)=((F(ii)+F(ii+1))/2)*(x(ii+1)-x(ii))
end
Area=sum(FF)/(M-2)
% plot(x(1:M),F(1:M))
% grid on
% y=fft(f(1:M))
% hold on 
% plot(x(1:M),y(1:M),'r*')

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Fourier Transform

clc
clear
M=100;
xxx0=-10;
xxxx0=10;
dx=(xxxx0-xxx0)/M;
xxx=xxx0:dx:xxxx0;
for ii=1:M;
xx(ii)=rand(1,1);                    %fluctuations of a random signal
x(ii)=xx(ii)*sin(xxx(ii));           %samples of a sinusoidal random signal
y(ii) = fft(x(ii));                       % Fourier transform of the signal
iy(ii) = ifft(y(ii));                      % inverse Fourier transform
x2(ii) = real(iy(ii));                   % chop off tiny imaginary parts
yy(ii)=norm(x(ii)-x2(ii));
end
plot(xxx(1:M),x(1:M))
grid on
hold on
plot(xxx(1:M),iy(1:M),'r-')

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Inverse Fourier Transform

Under construction.

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Waveform and Amplitude Spectrum

Under construction.

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Filtering Noise from Signals

Under construction.

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