# Square wave

## Type of non-sinusoidal waveform / From Wikipedia, the free encyclopedia

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A **square wave** is a 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.

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**Quick Facts**General information, General definition ...

Square wave | |
---|---|

General information | |

General definition | $x(t)=4\left\lfloor t\right\rfloor -2\left\lfloor 2t\right\rfloor +1,2t\notin \mathbb {Z}$ |

Fields of application | Electronics, synthesizers |

Domain, codomain and image | |

Domain | $\mathbb {R} \setminus \left\{{\tfrac {n}{2}}\right\},n\in \mathbb {Z}$ |

Codomain | $\left\{-1,1\right\}$ |

Basic features | |

Parity | Odd |

Period | 1 |

Antiderivative | Triangle wave |

Fourier series | $x(t)={\frac {4}{\pi }}\sum _{k=1}^{\infty }{\frac {1}{2k-1}}\sin \left(2\pi \left(2k-1\right)t\right)$ |

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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.