[gregfjohnson]

Here is an excellent resource:

https://ccrma.stanford.edu/~jos/

The first online book linked from the author's homepage is:

MATHEMATICS OF THE DISCRETE FOURIER TRANSFORM (DFT) WITH AUDIO APPLICATIONS SECOND EDITION

IMHO the author does a brilliant job of presenting the mathematics with rigor, but with accessible "on-ramps" via examples.

[howard941]

Wow. In all seriousness I regret I have only one up arrow to give for this guy's online stuff.

[52-6F-62]

Thank you! This is exactly the kind of applied maths I need to get myself to commit to learning what I (at least think) I want to learn.

Appreciate it!