Hey! First of all, thanks for reading :)
You can read about Spotify audio formats in their site, for example here.
As you can read, they are using the AAC format which uses Modified Discerte Cosine Transform, which is a sort of Fourier Transform under steroids. You can have a quick overview of how MDCT relates to Fourier Transform here.
For what about applications of Harmonic Analysis, I can suggest a book which I started reading back in my university days but I have never finished which is this.
As a rule of thumb, if you're not too much into mathematical details, going for resources for physicists or engineers is better: they tend to be more straight to the point and easier to approach. Having studied mathematics I shouldn't say so, but yeah, that's true :D
Hope I have helped a bit!
Thanks Manuel! These are excellent,
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