Up until this point, we’ve been talking about audio processing and synthesis in the time domain. Spectral processing takes place in the frequency domain. In the time domain, we represent sound as changing amplitude (y value) over time (x value). In the frequency domain, sound is represented as changing amplitude (y value) over frequency (x value). Two things are worth pointing out at this point. One, the property of the x axis is your domain; and two, neither domain represents both time and frequency. If you’re representing time you know nothing about frequency. Likewise, if you’re representing frequency you don’t have any time information.
To convert from a time domain representation of sound to a frequency domain representation, you use a process called the Fourier Transform. To reverse the process and convert from the frequency domain to the time domain you use an Inverse Fourier Transform.