A pulse wave or pulse train or rectangular wave is a non-sinusoidal waveform that is the periodic version of the rectangular function. It is held high a percent each cycle (period) called the duty cycle and for the remainder of each cycle is low. A duty cycle of 50% produces a square wave, a specific case of a rectangular wave. The average level of a rectangular wave is also given by the duty cycle. The pulse wave is used as a basis for other waveforms that modulate an aspect of the pulse wave, for instance:

Frequency-domain representation

The Fourier series expansion for a rectangular pulse wave with period T, amplitude A and pulse length \tau is where. Equivalently, if duty cycle is used, and : Note that, for symmetry, the starting time (t=0) in this expansion is halfway through the first pulse. Alternatively, x(t) can be written using the Sinc function, using the definition, as or with as

Generation

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.

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".