Hi
I have a function in frequency-domain, which is almost periodic (it oscillates, but not in a very consistent way). My teacher told me that if I Fourier transform this function, then I will be able to extract the approximate period. Do you have any idea of what he is talking about?
Sincerely,
Niles.
Yes: the frequency with most contribution is indeed , and the corresponding period is .
For a better example (one where there is not an exact periodicity), compute the Fourier transform of the function that equals when and 0 elsewhere. This function is not perdiodic, hence you have no rigorous way to define a period. However, you'll see (computation is simple, if I remember well) that the Fourier transform is maximum at (like above), as it "should be". I don't know if there are other simple examples, where computations can be done by hand, but you can try numerical experiments.
Thanky you very much. I really appreciate your help.
I have known about Fourier transformations for quite some time now, but it is the very first time that I read about these things. But it is interesting.
Again, thank you; it really means alot. For now I will work on some examples to get familiar with the concept. If there is any trouble, I will let you know.
Sincerely,
Niles.
Note that if is a frequency, then is also a frequency, etc, hence in your case the frequency is 1.
This case is no different from Fourier series: if a function is periodic with frequence , its Fourier transform is a multiple of a sum of peaks at integer multiples of .
In physics, the square modulus of the Fourier transform gives the "energy" of a given frequence. The fundamental frequency would be (loosely speaking) that with the most energy: either the highest peak (if sum of deltas) or the highest integral , which is to say, if is continuous, the highest value of .