Order | ||||||
---|---|---|---|---|---|---|

0 | ½ | 1 | 2 | |||

Slope / oct | 0 dB | −3 dB | −6 dB | −12 dB | ||

Exciter | Noise | White | Pink | Red | ||

Evens | Pulse | Sawtooth | Parabolic wave(?) | |||

Odds | Alternating pulse(?) | Square | Triangle | |||

Generating discontinuity | impulse | step | knee |

The above six basic periodic waveforms can be digitally formed purely from periodically repeating samples of windowed, sinc‐filtered discontinuities of the form according to the order of the waveform, interpolated with linear or quadratic samples as appropriate to maintain zero DC offset. For even waveforms, the discontinuities should be repeated with the same polarity; for odd waveforms, alternating polarity.

Note that mixing the odd waveform of one order with a suitably scaled even waveform of the same order an octave up, results in the even waveform of the same order at the base frequency.

Of further note, and not noted in the table above, is that odd
waveforms of order `N` can be produced from even waveforms of
order `N`−1 by convolution with the rectangular function of a
half-period width. Notably, convolution of the pulse waveform with a
rectangular function of lesser width produces the pulse‐width
modulation waveform family; similar convolution of the sawtooth
waveform produces the skewed‐triangle waveform family.

Note that, when the base frequency of a perfectly periodic waveform
exactly subdivides the sampling frequency, no *aharmonic*
aliasing occurs. (*Harmonic* aliasing still occurs, but this
is much less noticeable.)