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Note : Answers with dimensions (cy/mm) instead of (Hz) would be greatly appreciated!

I have looked into unit of fft(DFT) x axis and units on x axis after FFT , but I couldn't find exactly what I'm looking for. So, I decided to write my own question.

I have an object in the real world that has a width of 3mm that scans a bigger object of width 310mm. I can model this as a linear system with a convolution process with a rectangular function of width 3mm as follows:

g(x) = f(x) * rect(x/3mm)

where f(x) is the 310mm object, and g(x) is the output of the scanned object. In MATLAB, I'm trying to simulate this effect, so I imported the 310mm object as a high resolution array with each point in the array corresponds to 1mm.

Now, to model the rect(x/3mm) I'm thinking of two way to do it, and I'm not sure which one is correct.

1- Is to say that rect(x/3mm) is equal to 3 points of the high resolution array, then can be created as a kernel of zeros of the same size as the high resolution object with only 3 point of 1's. Now the actual spacing between the kernel point = 1mm. How can you show the proper FFT scale of this rect(x/3mm) model?

2- I can define in MATLAB 

d = 3; % in mm
value = 2;
spacing = 0.01;
x = -value: spacing : value - spacing
y = rect(x/d);

the second way will provide me with a rect(x/3mm) that can be coarsely of finely created depending on spacing or value, but the first way was only 3 points. How can you show the proper FFT scale of this rect(x/3mm) model?

Which of the two methods is the correct way of doing it?

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  • see my answer : http://stackoverflow.com/questions/13054363/matlab-fast-fourier-transform-fft-for-time-and-speed/13054749#13054749 – bla Oct 14 '13 at 07:27
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    This question appears to be off-topic because it is about Fourier analysis \ signal processing theory and not programming – bla Oct 14 '13 at 07:28
  • I saw your answer, and I know that df*dx*N = 1, then I can plot my answers from -Nyq_rate: Nyq_rate. But the 2 ways I mentioned above can results in different answers. I tried to introduce the background before the programming question for better understanding. That's why probably you felt it is off-topic. It is mainly about which way is correct and how to deal with each way in terms of scaling! Thank you :) – mxy Oct 14 '13 at 07:38

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