Is this achieved through applying Fourier transforms, or through some other means?
Just by the final result in this slide it seems like the signals expressed as a superposition of frequencies will always end up repeating with some interval. Considering how an audio clip may start and end very drastically, I don't think an entire loop of the audio file is a valid continuous loop. Then how are these repeating superpositions actually turned into seemingly pattern-less audio signals?
Is the decomposition always unique? What are the implications if it is not?
If a decomposition is in infinite series, how can we approximate it in computing?
The Fourier series are generally infinite. In practice, how many terms should we use to approximate a function f so that this approximation can be considered acceptable?