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{{about|a pulse wave form|a heart beat|Pulse}}
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{{about|a rectangular pulse train|a Dirac pulse train|Sampling function}}
{{Other uses|Pulse (disambiguation)}}
 
{{Refimprove|date=June 2013}}
 
[[File:Dutycycle.svg|thumb|350px|The shape of the pulse wave is defined by its duty cycle D, which is the ratio between the pulse duration (<math>\tau</math>) and the period (T)]]
 
A '''pulse wave''' or '''pulse train''' is a kind of [[non-sinusoidal]] [[waveform]] that is similar to a [[square wave]], but does not have the symmetrical shape associated with a perfect square wave. It is a term common to [[Analog synthesizer|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 (sometimes called pulse-width modulation) for a more dynamic timbre.<ref>http://www.soundonsound.com/sos/feb00/articles/synthsecrets.htm</ref>
The pulse wave is also known as the '''rectangular wave''', the [[Periodic function|periodic]] version of the [[rectangular function]].
 
The [[Fourier series]] expansion for a rectangular pulse wave with period {{math|''T''}} and pulse time {{math|''τ''}} is
 
:<math>f(t) = \frac{\tau}{T} + \sum_{n=1}^{\infty} \frac{2}{n\pi} \sin\left(\frac{\pi n\tau}{T}\right) \cos\left(\frac{2\pi n}{T} t\right)</math>
 
Note that, for symmetry, the starting time ({{math|''t'' {{=}} 0}}) in this expansion is halfway through the first pulse. The phase can be offset to match the accompanying graph by replacing {{math|''t''}} with {{math|''t'' - ''τ''/2}}.
 
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.
 
==See also==
*[[Rectangular function]]
*[[Sampling function]]
*[[Pulse-width modulation]]
*[[Sine wave]]
*[[Triangle wave]]
*[[Square wave]]
 
==References==
{{Reflist}}
 
{{DEFAULTSORT:Pulse Wave}}
[[Category:Waves]]
 
 
{{Electronics-stub}}

Latest revision as of 00:18, 3 April 2014

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