The Discrete Fourier Transform

Microphones produce digital samples from analog signals. The samples are in the time domain, which means that the samples are viewed as a function of time. However, it is much more intuitive and useful to manipulate audio by modifying its individual frequencies. To do this, the sequence of samples must be converted to the frequency domain. The process of converting from the time domain to the frequency domain is non-trivial yet extremely important for the vast majority of audio applications.