Class of audio signals
A sound can be viewed as a mathematical function of air pressure, with time as a free variable. Such a function satisfies the Dirichlet conditions. According to the ideas expressed by Jean-Baptiste Joseph Fourier such a function can be considered a weighted sum of simple sine waves.
In some cases the frequency components of a sound have a simple harmonic relationship. The sawtooth wave for instance, is produced by summing a sine wave with a certain base frequency with all sine waves at integer multiples of that base frequency at exponentially decreasing amplitudes. Such a waveform, one that can be expressed with a straightforward mathematical formula, is considered a simple waveform. Other simple waveforms include the square wave, the triangle wave and the sine wave itself.
Other waveforms, like a recording of Beethoven's third or Slayer's Reighn in blood, can only be expressed as a Fourier series with unpredictable coefficients. They are considered complex waveforms.