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Triangle wave

A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.

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Key facts & relationships

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Codomain
[ − 1 , 1 ] {\displaystyle \left[-1,1\right]}
Derivative
Square wave
Domain
R {\displaystyle \mathbb {R} }
Fields of application
Electronics, synthesizers
Fourier series
x ( t ) = − 8 π 2 ∑ k = 1 ∞ ( − 1 ) k ( 2 k − 1 ) 2 sin ⁡ ( 2 π ( 2 k − 1 ) t ) {\displaystyle x(t)=-{\frac {8}{{\pi }^{2}}}\sum _{k=1}^{\infty }{\frac {{\left(-1\right)}^{k}}{\…
General definition
x ( t ) = 4 | t − ⌊ t + 3 / 4 ⌋ + 1 / 4 | − 1 {\displaystyle x(t)=4\left\vert t-\left\lfloor t+3/4\right\rfloor +1/4\right\vert -1}

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Overview

Definitions

Arc length

Advanced semantic analysis

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Map overview Semantic statistics

Triangle wave

Nodes26
Edges25
Triples24
Avg. degree1.92
Density0.076923
Components1

How this topic connects Entity context

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Triangle wave

Top relations

related to References · 4
Triangle wave → Eric, Fourier Series, MathWorld, Weisstein
related to Harmonics · 3
Triangle wave → It, N-1, The
related to Definition · 2
Triangle wave → For, This
related to Expression in trigonometric functions · 2
Triangle wave → The, This
Codomain · 1
Triangle wave → [ − 1 , 1 ] {\displaystyle \left[-1,1\right]}
Derivative · 1
Triangle wave → Square wave
Domain · 1
Triangle wave → R {\displaystyle \mathbb {R} }
Fields of application · 1
Triangle wave → Electronics, synthesizers
Fourier series · 1
Triangle wave → x ( t ) = − 8 π 2 ∑ k = 1 ∞ ( − 1 ) k ( 2 k − 1 ) 2 sin ⁡ ( 2 π ( 2 k − 1 ) t ) {\displaystyle x(t)=-{\frac {8}{{\pi }^{2}}}\sum _{k=1}^{\infty }{\frac {{\left(-1\right)}^{k}}{\…
General definition · 1
Triangle wave → x ( t ) = 4 | t − ⌊ t + 3 / 4 ⌋ + 1 / 4 | − 1 {\displaystyle x(t)=4\left\vert t-\left\lfloor t+3/4\right\rfloor +1/4\right\vert -1}

Important terminology Word statistics

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Important terminology

wave triangle displaystyle left right frac square harmonics period sin pi lfloor rfloor -1 value amplitude number frequency expressed odd

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Triangle waveCodomain[ − 1 , 1 ] {\displaystyle \left[-1,1\right]}1.00infobox
Triangle waveDerivativeSquare wave1.00infobox
Triangle waveDomainR {\displaystyle \mathbb {R} }1.00infobox
Triangle waveFields of applicationElectronics, synthesizers1.00infobox
Triangle waveFourier seriesx ( t ) = − 8 π 2 ∑ k = 1 ∞ ( − 1 ) k ( 2 k − 1 ) 2 sin ⁡ ( 2 π ( 2 k − 1 ) t ) {\displaystyle x(t)=-{\frac {8}{{\pi }^{2}}}\sum _{k=1}^{\infty }{\frac {{\left(-1\right)}^{k}}{\…1.00infobox
Triangle waveGeneral definitionx ( t ) = 4 | t − ⌊ t + 3 / 4 ⌋ + 1 / 4 | − 1 {\displaystyle x(t)=4\left\vert t-\left\lfloor t+3/4\right\rfloor +1/4\right\vert -1}1.00infobox
Triangle waveParityOdd1.00infobox
Triangle wavePeriod11.00infobox
Triangle waveRoot{ n 2 } , n ∈ Z {\displaystyle \left\{{\tfrac {n}{2}}\right\},n\in \mathbb {Z} }1.00infobox
Triangle waveis anon-sinusoidal waveform named for its triangular shape0.90text
Triangle waverelated to Arc lengthThe0.60section
Triangle waverelated to DefinitionThis0.60section

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    Min side: 3
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