HN Academy

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.

I recommend Prandoni & Vetterli's coursera class on Signal processing[1]. They have really made an effort to teach this in an intuitive manner instead of just throwing equations at you. This was the course where I finally really understood Fourier transforms in a visual way.

The other course I recommend is the Audio Signal processing class by Xavier Serra[2] This is a practical class with lots of hands on programming examples and introduction to useful open-source software tools.

[1] https://www.coursera.org/learn/dsp [2] https://www.coursera.org/learn/audio-signal-processing

A couple of things that people who like this might also be interested in:

Coursera.org is currently running a course called "Audio Signal Processing for Music Applications" which I believe uses python. It's in its second week, so you have time to catch up. https://www.coursera.org/course/audio

http://aubio.org/ is a library that does note onset detection, pitch detection, beat / tempo tracking and various other things. It has python bindings.