I recommend Coursera Digital Signal Processing by Martin Vetterli https://www.coursera.org/learn/dsp. He does a good job of explaining the math behind the DFT. Any finite signal can be expressed as a linear combination of complex exponentials - that was the aha! moment for me.

Once you have that under your belt you might find Audio Signal Processing for Music Applications by Xavier Serra a fun course to complete https://www.coursera.org/learn/audio-signal-processing.