The standard Fourier Transform \begin{equation*} (\mathcal{F} f)(\omega)=\frac{1}{\sqrt{2 \pi}} \int d t e^{-i \omega t} f(t) \end{equation*} gives a representation of the frequency content of $f(t)$ but no information about the time-localization. I read this sentence in a book (the popular book by Daubechies, "Ten Lectures on Wavelets") but... why? I would like to read an example that explain in detail this sentence.
2026-04-30 03:15:37.1777518937
Why is time-localization not captured by standard Fourier Transform?
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