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You're describing the DTFT (discrete-time Fourier transform), not the DFT. https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform https://en.wikipedia.o

You're describing the DTFT (discrete-time Fourier transform), not the DFT. https://en.wikipedia.org/wiki/Discrete-time_Fourier_transform https://en.wikipedia.org/wiki/Discrete-time_Fourier_transfor... Pedantics aside: Spectrum analyzers are computing DFTs over a finite window, and it's perfectly reasonable to think of these as (an approximation of) power spectral density changing over time.

jameshart 3y ago
Right. But if you think Fourier transforms produce a function of ‘power spectral density over time’ you are on a road to misunderstanding. Or even if you think that it makes sense to talk about the Fourier transform ‘at a moment in time’. The thing I am railing against here is the idea that you can just look at a spectrogram to grasp Fourier. You can’t. It is an advanced application of Fourier transforms that creates a visualization of power spectral density over time but it is not a (simple) Fourier transform of the underlying data.