Is this achieved through applying Fourier transforms, or through some other means?

Alan7996

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?

fzeng

Is the decomposition always unique? What are the implications if it is not?

bobzhangyc

If a decomposition is in infinite series, how can we approximate it in computing?

jonasjiang

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?

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?