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In wikipedia they say that the absolute value of the Fourier transform is the amount of frequency of the original function. Could someone explain what does it mean ? I don't understand what could be the frequency of a non periodic function. With this concept, taking the frequency of a periodic function should gives its period, but since such a function is not $L^1$, it doesn't make any sense. So, what do they mean by : "frequency" for a non periodic function ? But maybe there is an other explanation ?

Dylan
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    If everything converges and $f(x) = \int_{-\infty}^\infty F(\xi) e^{2i \pi \xi x}d\xi$ then $f(x) = \sum_k e^{2i \pi x k/N} f_{k,N}(x)$ where $f_{k,N}(x) = \int_0^{1/N} F(\xi+k/N) e^{2i \pi \xi x}d\xi$ is smooth and slowly varying, so that locally $e^{2i \pi x k/N} f_{k,N}(x)$ looks like a complex sine of frequency $ k/N$ – reuns Feb 03 '19 at 12:38

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