Phase offset modulation works by overlaying two instances of a periodic
waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronic ...
on top of each other. (In
software synthesis, the waveform is usually generated by using a
lookup table
In computer science, a lookup table (LUT) is an array that replaces runtime computation with a simpler array indexing operation. The process is termed as "direct addressing" and LUTs differ from hash tables in a way that, to retrieve a value v wi ...
.) The two instances of the waveform are kept slightly out of sync with each other, as one is further ahead or further behind in its cycle. The values of both of the waveforms are either multiplied together, or the value of one is subtracted from the other.
This generates an entirely new waveform with a drastically different shape. For example, one
sawtooth (ramp) wave subtracted from another will create a
pulse wave
A pulse wave or pulse train is a type of non-sinusoidal waveform that includes square waves (duty cycle of 50%) and similarly periodic but asymmetrical waves (duty cycles other than 50%). It is a term used in synthesizer programming, and is ...
, with the amount of offset (i.e. the difference between the two waveforms' starting points) dictating the
duty cycle
A duty cycle or power cycle is the fraction of one period in which a signal or system is active. Duty cycle is commonly expressed as a percentage or a ratio. A period is the time it takes for a signal to complete an on-and-off cycle. As a formu ...
. If you slowly change the offset amount, you create
pulse-width modulation
Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a method of reducing the average power delivered by an electrical signal, by effectively chopping it up into discrete parts. The average value of voltage (and current) fed ...
.
Using this technique, not only can a ramp wave create pulsewidth modulation, but any other waveform can achieve a comparable effect.
Wave mechanics
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