How does an FFT work on an image? Can anyone explain how exactly FFT transforms the image from spatial to frequency domain using each pixel of the image, step by step? Does anybody have a detailed explanation?
MATLAB: How FFT works on an image
dftfftImage Processing ToolboxMATLAB
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Not entirely. The posted image is the plot of the two-sided Fourier transform after using the fftshift function. The result is that the frequency axis is not correct. (Note that a 2D fft (fft2) is usually applied to images and similarly-constructed matrices. The 1D fft is correct here.)
Try this:
D = load('matlab.mat');mat = D.mat;t = 0:numel(mat)-1; % Time Vector (Units: Time Units)
Ts = mean(diff(t)); % Sampling Time Interval
Fs = 1/Ts; % Sampling Frequency
Fn = Fs/2; % Nyquist Frequency
L = numel(t); % Signal Length
FTmat = fft(mat)/L; % Fourier Transform
Fv1 = linspace(0, 1, fix(L/2)+1)*Fn; % Frequency Vector - One-Sided Fourier Transform (Units: Cycles/Time Unit)
Iv = 1:numel(Fv1); % Index Vector
figureplot(Fv1, abs(FTmat(Iv))*2)gridtitle('One-sided Fourier Transform')xlabel('Frequency')ylabel('Amplitude')Fv2 = linspace(-Fn, +Fn, L); % Frequency Vector - Two-Sided Fourier Transform (Units: Cycles/Time Unit)
figureplot(Fv2, fftshift(abs(FTmat)))gridtitle('Two-Sided Fourier Transform')xlabel('Frequency')ylabel('Amplitude')producing:
Not sure what you're looking for. Since your second image has a circular mask multiplied by the first image, your second spectrum will be the same as the first spectrum, just convolved with a narrow sombrero function.
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