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Square wave (waveform)
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{{Use dmy dates|date=July 2023}} {{short description|Type of non-sinusoidal waveform}} {{About|the waveform|a type of ocean wave also known as a square wave|Cross sea}} {{refimprove|date=December 2019}} {{Infobox mathematical function | name = Square wave | image = Waveforms.svg | imagesize = 400px | imagealt = Sine, square, triangle, and sawtooth waveforms | caption = [[Sine wave|Sine]], square, [[triangle wave|triangle]], and [[sawtooth wave|sawtooth]] waveforms | general_definition = <math>x(t) = 4 \left\lfloor t \right\rfloor - 2 \left\lfloor 2 t \right\rfloor + 1, 2 t \notin \mathbb{Z}</math> | fields_of_application = Electronics, synthesizers | domain = <math>\mathbb{R} \setminus \left\{ \tfrac{n}{2} \right\}, n \in \mathbb{Z}</math> | codomain = <math>\left\{ -1,1 \right\}</math> | parity = Odd | period = 1 | antiderivative = [[Triangle wave]] | fourier_series = <math>x(t) = \frac{4}{\pi} \sum_{k=1}^{\infty} \frac{1}{2 k - 1} \sin \left( 2 \pi \left(2 k - 1 \right) t \right)</math> }} {{Listen | filename = 220 Hz anti-aliased square wave.ogg | title = Square wave sound sample | description = 5 seconds of square wave at 220 Hz | filename2 = 220 Hz sine wave.ogg | title2 = Sine wave sound sample | description2 = For comparison, five seconds of a 220 Hz [[sine wave]]. | format = [[Ogg]] }} A '''square wave''' is a [[non-sinusoidal waveform|non-sinusoidal periodic waveform]] in which the amplitude alternates at a steady [[frequency]] between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square wave, the transitions between minimum and maximum are instantaneous. The square wave is a special case of a [[pulse wave]] which allows arbitrary durations at minimum and maximum amplitudes. The ratio of the high period to the total period of a pulse wave is called the [[duty cycle]]. A true square wave has a 50% duty cycle (equal high and low periods). Square waves are often encountered in [[electronics]] and [[signal processing]], particularly [[digital electronics]] and [[digital signal processing]]. Its [[stochastic]] counterpart is a [[two-state trajectory]].
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