fourier transform of a pattern

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Rehan
Rehan 2015-11-5
编辑： Rehan 2015-11-8
Let's say we have a periodic pattern (1D) with black and white stripes. The period is p. We can move the pattern along the pattern direction. Each time we move only p/3. Can you write the Fourier transform of this pattern and what happens when we move the pattern?
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Image Analyst
Image Analyst 2015-11-5
Yes, I can. Why don't you try it and see?
Rehan
Rehan 2015-11-5
i need little clue,because i am not good at dft

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Image Analyst
Image Analyst 2015-11-5
Use ones(), zeros(), and repmat() to make up a series of stripes. Then call fft(). I think all I have are fft2 demos on 2-D images.

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Walter Roberson
Walter Roberson 2015-11-5
No, with that information you cannot write the Fourier transform.
Consider the pattern
1001110011100111001110011100111001110011
The period is 5: the pattern is repeats of 10011. But that is going to have different fourier transform compared to
1110011100111001110011100111001110011100
which is also period 5.
The period of a pattern does not tell you anything about the complexity of the pattern.
The effect of the movement is going to depend upon the whether the period is divisible 3, which is not given.
If the period is divisible by 3, then each location will cycle in value every 3. You can predict that it will go through one of the 8 patterns, 000, 001, 010, 011, 100, 101, 110, or 111, but each location might go through a different pattern, not just a different phase of the same pattern. For example if the pattern is 010011010 then the period is 9 and a movement of 3 at a time would produce 010011010 then 011010010 then 010010011. Notice that the first location is always 0, the second is always 1, and the third goes 010, so the fft of the first or second location would have only the DC offset (first location) nonzero but the third location would have a different result.
If the period is not divisible by 3, then each bit will reach each position with period 3*p (I think it is.)
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Rehan
Rehan 2015-11-8
thanks,both answers helped me in different aspects,i want to accept both answers but i don't know how, i accepted first and second option disappeared . but i accept both answers,because both have given me good idea in different aspects. Thanks to both of you :)

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