[CGMthrowaway]

It's a Copy>Paste Special>Transpose on a waveform, converting Rows/Columns that are time/amplitude (with wavelength embedded) into Rows/Columns that are frequency/amplitude (for a snapshot in time).

People love to go on about how brilliant it is and they're probably right but that's how I understand it.

[TheOtherHobbes]

Pretty much, but phase is also included. Which matters for some things.

[bobmcnamara]

But mostly not for ears it turns out!

Phase matters for some wideband signals, but most folks struggle to tell apart audio from hilbert-90-degree-shifted-audio

[xeonmc]

Phase is required if it is to be a reversible transform. Otherwise would just be a Functional.