Sampling frequency for image

Question

Dominik Deml 2023-6-24

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1987608-sampling-frequency-for-image

回答： Image Analyst 2023-6-24

采纳的回答： Image Analyst

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I have an 30 x 30 pixel image that looks like this:

The spatial frequency is 0.1 (1/pixel)

The code to produce this image:

x = 0:1:30;
y = 0:1:30;
[X, Y] = meshgrid(x, y);
fx = 0.1;        % spatial frequency [1/Pixel]  
p = cos(2*pi*(fx*X + 0*Y)) + 1;
figure;
imshow(p);
colormap('gray');

Now I want to do the fft of the first row of my image:

fs = 1; % sampling frequency
% compute FFT coefficients, norm with the length of the signal
FFTtmp = fft(p(1, :))/length(p(1, :));
% discard redundant coeffcients (n could be odd!)
n = length(p(1, :))/2;
spectrum_signal = FFTtmp(1:floor(n)+1);    
% correct values other than DC and fs/2
spectrum_signal(2:end-1)   = spectrum_signal(2:end-1)*2;    
% create frequency vector (frequency step is fs/length(signal) )
f=(0:floor(n))/n * fs/2;
stem(f, abs(spectrum_signal));

The amplitude spectrum looks like this:

But this is not the result I expected.

I expected only 2 frequencies to be there, 0 and 0.1 (1/Pixel).

So my question is, which sampling frequency do I have to choose?

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Answer 1

Image Analyst 2023-6-24

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1987608-sampling-frequency-for-image#answer_1261818

Why do you expect only two spatial frequencies. You know that you don't have an infinite cosine wave, right? You know that it is truncated by a rectangular window, right? And you know that multiplication of a spatial signal by a rect function will have the effect of convolution of the cosine spectrum with the spectrum of the rect function, which is a sinc function, right? The convolution will give power at frequencies other than the two corresponding to an infinitely long cosine function. So, no, there will not be just two frequencies.