Properties of complex periodic one-dimensional signals

A complex signal is the sum of the amplitudes of its component signals for each value of the independent variable. These amplitudes are related to the frequency and the phase of the signal. In the following equation, is the amplitude of signal i at time t, is the frequency of signal i at time t, and is the phase of signal i at time t; the resulting values (the instantaneous amplitudes) of each signals i from 1 to N at any time t are added, and the value of the complex signal at time t is the result.

1. The values of the signals may be systematically related. If the frequencies can be modelled as integer multiples of the lowest frequency (i.e. 1f, 2f, ... nf,i.e. a harmonic series, then the signal is a harmonic signal. A special kind of harmonic series is the Fourier series, in which the amplitude of the harmonics varies with the number of the harmonic.
2. A square wave is approximated by a series including only the odd-numbered harmonics.
3. A sawtooth (triangular) waveform is approximated by a series including only the even-numbered harmonics. The waveform produced at the glottis is approximately a sawtooth.