Sawtooth Wave


The sawtooth wave, called the "castle rim function" by Trott (2004, p. 228), is the periodic function given by


where frac(x) is the fractional part frac(x)=x-|_x_|, A is the amplitude, T is the period of the wave, and phi is its phase. (Note that Trott 2004, p. 228 uses the term "sawtooth function" to describe a triangle wave.) It therefore consists of an infinite sequence of truncated ramp functions concatenated together.

The sawtooth wave is implemented in the Wolfram Language as SawtoothWave[x].

If phi=0, A=1, and T=2L, then the Fourier series is given by


and the function can be written


where |_x_| is the floor function.

See also

Fourier Series--Sawtooth Wave, Fractional Part, Ramp Function, Square Wave, Staircase Function, Triangle Wave

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Spanier, J. and Oldham, K. B. An Atlas of Functions. Washington, DC: Hemisphere, p. 74, 1987.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004.

Cite this as:

Weisstein, Eric W. "Sawtooth Wave." From MathWorld--A Wolfram Web Resource.

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