Pulse wave


A pulse wave or pulse train is a kind of non-sinusoidal waveform that includes square waves and similarly periodic but asymmetrical waves. It is a term common to synthesizer programming, and is a typical waveform available on many synthesizers. The exact shape of the wave is determined by the duty cycle of the oscillator. In many synthesizers, the duty cycle can be modulated for a more dynamic timbre.
The pulse wave is also known as the rectangular wave, the periodic version of the rectangular function.
The average level of a rectangular wave is also given by the duty cycle, therefore by varying the on and off periods and then averaging these said periods, it is possible to represent any value between the two limiting levels. This is the basis of pulse width modulation.
The Fourier series expansion for a rectangular pulse wave with period and pulse time is
Note that, for symmetry, the starting time in this expansion is halfway through the first pulse. The phase can be offset to match the accompanying graph by replacing with.
A pulse wave can be created by subtracting a sawtooth wave from a phase-shifted version of itself. If the sawtooth waves are bandlimited, the resulting pulse wave is bandlimited, too. Another way to create one is with a single ramp wave and a comparator, with the ramp wave on one input, and a variable DC threshold on the other. The result will be a precisely controlled pulse width, but it will not be bandlimited.

Applications

The harmonic spectrum of a pulse wave is determined by the duty cycle. Acoustically, the rectangular wave has been described variously as having a narrow/thin, nasal/buzzy/biting, clear, resonant, rich, round and bright sound. Pulse waves are used in many Steve Winwood songs, such as "While You See a Chance".
In digital electronics, a digital signal is a pulse train, a sequence of fixed-width square wave electrical pulses or light pulses, each occupying one of two discrete levels of amplitude. These electronic pulse trains are typically generated by metal–oxide–semiconductor field-effect transistor devices due to their rapid on–off electronic switching behavior, in contrast to BJT transistors which slowly generate signals more closely resembling sine waves.