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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. 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 This is a practical class with lots of hands on programming examples and introduction to useful open-source software tools.
Is is just me being a n00b or are there a few errors in the equations? Like the exponential definitions of sin and cos, a missing negative sign in proof of m≠n, maybe more later not sure. Somewhat perplexing for someone learning the stuff BUT then again, I'm in medicine; so it might actually just be me.
Relevant for other learners is the digital signal processing lectures on Coursera, highly recommended with python notebooks and quizzes. https://www.coursera.org/learn/dsp
⬐ mjflYou are correct on the sine and cosine thing, the minus is switched. Will fix, thanks.
i would presume https://www.coursera.org/course/dsp which was pretty good when I did it - https://www.coursera.org/course/images also covered some similar things
⬐ elcapitanThat looks like it, great, thanks.
The reason why I'm asking instead of searching on Coursera is that Coursera has become increasingly hard to search, at least in my view, so it's easier to ask directly.
For anyone interested in DSP, the Coursera DSP class is superbly well done: https://www.coursera.org/course/dsp
There's a coursera session on digital signal processing going on right now, figured I'd take a crack at it: https://www.coursera.org/course/dsp
⬐ heldervascHave anyone tried this course? i'm thinking about attending this course but i don't know if it is worth.