Although the theory of Fourier series is by now 200 years old only the advent of computers and the development of the fast Fourier transform algorithm FFT by Cooley-Tukey (1965) provided the tools to enter the digital area. First digital recordings of sound on CDs (instead of records of plastic or on tape) where made possible, then digital still images followed, now we are down-loading movies from the internet at do ditigal recordings using our mobile phones.

The mathematical background is the so-called sliding-window Fourier transform, which produces a spectrogram of the signal under analysis. The Windows-Media-Player allows to visualize this time-variant spectrogram, i.e. the change of the frequency distribution in the signal over time. In fact, it is an alternative description to musical score, with the advantage of perfect coding of the actual sound, and the extra chance of manipulating it. This is done in practice, e.g. in order to compress audio-signals using the MP3 compression standard. But also the transmission of information from the sending station to the mobile phone can be understood mathematically using such time-frequency methods.
Using the two-dimensional Fourier transform is part of the JPEG compression standard for digital images. More recent methods involve so-called wavelet systems, which allow to decompose a signal into course and fine details.