To Have and Have Notch. It is customary to remark that the Fourier transform (FT) decomposes a transient time signal (data) into independent harmonic components and, therefore, has exact frequency localization and no time localization. In other words, FT can precisely detect which frequencies reside in the data, but yields no information about the time position of signal features. Let's investigate this claim by considering the FT impulse response. Warning (for the faint of heart): math ahead.

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