[frisco]

Imagine you want to calculate what frequencies are present in a sound. At the width of the time window you are looking at goes to zero, you just have a single point. There's no frequency content of a single point! It's just a number. As you look at a longer time window, you can see what frequencies are present over the window, but you lose some sense of time "resolution" over which that is meaningful. This is fundamental and inherent in the Fourier transform.

Put differently, you can't have a signal that is simultaneously both "band-limited" and "time-limited". Other conjugate variables, like position and momentum, work the same way.

[jacquesm]

That's a beautiful way to describe this.

[spiritplumber]

I tried to FFT an audio sample with a single value and the FFT app barfed.