A sound spectrum is the complete set of frequency components with their amplitudes and phases

The spectrum of a sound is its description in the frequency domain: the list of all frequency components present, each with its own amplitude and phase. Waveform (time domain) and spectrum (frequency domain) are two complete and equivalent descriptions of the same sound. A spectrum can be visualized as a bar chart: frequency on the x-axis, amplitude on the y-axis; phase information is usually shown separately. Synthesizing a sound additively means specifying its spectrum; filtering a sound means reshaping its spectrum. Every sound, natural or synthesized, has a unique spectrum that contributes to its timbre.

Examples

A 440 Hz sawtooth wave has spectral peaks at 440, 880, 1320, 1760 Hz with amplitudes 1, 0.5, 0.33, 0.25 (the harmonic series). The spectrum of white noise is essentially flat — equal amplitude at all frequencies.

Assessment

Describe the spectrum of a 100 Hz square wave: which harmonics are present, and which are absent? Why?