# Frequency decomposition

For some signals, particularly natural signals like voice, music, and images, finding a concise and precise definition of the signal can be difficult. In such cases, we try to model signals as compositions of simpler signals that we can more easily model.**Psychoacoustics** is the study of how humans hear sounds. Pure
tones and their frequency turn out to be a very convenient way to describe
sounds. Musical notes can be reasonably accurately modeled as combinations
of relatively few pure tones (although subtle properties of musical sounds,
the *timbre* of a sound, are much harder to model accurately).

When studying sounds, it is reasonable on psychoacoustic grounds to decompose the sounds into sums of sinusoids. It turns out that the motivation for doing this extends well beyond psychoacoustics. Pure tones have very convenient mathematical properties that make it useful to model other types of signals as sums of sinusoids, even when there is no psychoacoustic basis for doing so. For example, there is no psychoacoustic reason for modeling radio signals as sums of sinusoids.

Consider the sounds you can generate using the following applet:

The range of frequencies covers one octave, ranging from 440Hz to 880
Hz. "**Octave**" is the musical term for a factor of two in frequency.