SquareWave
SquareWave[x]
gives a square wave that alternates between and
with unit period.
SquareWave[{y1,y2},x]
gives a square wave that alternates between y1 and y2 with unit period.
Examples
open allclose allBasic Examples (3)
Plot over a subset of the reals:
SquareWave is a piecewise function over finite domains:
Scope (25)
Numerical Evaluation (4)
SquareWave[x] always returns an exact result:
SquareWave[{min,max},x] generally tracks the precision of {min,max}:
Evaluate efficiently at high precision:
SquareWave threads over lists in the last argument:
Specific Values (3)
Find a value of x for which the SquareWave[{2,-3},x]=2:
Visualization (4)
Plot the SquareWave function:
Visualize scaled SquareWave functions:
Visualize SquareWave functions with different maximum and minimum values:
Plot SquareWave in three dimensions:
Function Properties (5)
Function domain of SquareWave:
It is restricted to real inputs:
Function range of SquareWave:
SquareWave is periodic with period 1:
SquareWave is an odd function:
Differentiation and Integration (4)
First derivative with respect to :
Derivative of the two-argument form with respect to :
Compute the indefinite integral using Integrate:
Verify the anti-derivative away from the the singular points:
Series Expansions (5)
Since SquareWave is odd, FourierTrigSeries gives a simpler result:
The two results are equivalent:
FourierCosSeries of a scaled SquareWave:
Taylor series at a smooth point:
Properties & Relations (3)
Use FunctionExpand to expand SquareWave in terms of elementary functions:
Use PiecewiseExpand to obtain piecewise representation:
Possible Issues (1)
SquareWave is only defined on real numbers:
Text
Wolfram Research (2008), SquareWave, Wolfram Language function, https://reference.wolfram.com/language/ref/SquareWave.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 2008. "SquareWave." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SquareWave.html.
APA
Wolfram Language. (2008). SquareWave. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SquareWave.html