Kevin Wampler wrote:

> There's another argument that can lead you to the same conclusion that 
> you can't approximate any function over the reals with a Fourier 
> transform, and that's to note that the cardinality of the number of 
> possible Fourier representations is smaller than the cardinality of the 
> number of possible functions on the reals, so there have to be some 
> functions that you can't represent.

Sure. For example, you might have a partial function that isn't defined 
at certain points.

None of this really interests me that much, because in the specific 
instance I'm looking at [processing digital audio and video] there 
aren't any such functions to worry about.

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