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**Laurent** For a better example (one where there is not an exact periodicity), compute the Fourier transform of the function that equals $\displaystyle \sin x$ when $\displaystyle x\in[-a,a]$ 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 $\displaystyle 1$ (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.