Pulse wave
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: The Fourier series expansion for a rectangular pulse wave with period
and pulse length
π
π n
2 π n f t
Equivalently, if duty cycle
ω = 2 π f
π
π n d
Note that, for symmetry, the starting time (
) in this expansion is halfway through the first pulse.
can be written using the Sinc function, using the definition
sin π x
π x
2 π n f t
2 π n f t
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.
The harmonic spectrum of a pulse wave is determined by the duty cycle.
[2][3][4][5][6][7][8][9] Acoustically, the rectangular wave has been described variously as having a narrow[10]/thin,[11][3][4][12][13] nasal[11][3][4][10]/buzzy[13]/biting,[12] clear,[2] resonant,[2] rich,[3][13] round[3][13] and bright[13] sound.
Pulse waves are used in many Steve Winwood songs, such as "While You See a Chance".
