Sawtooth Wave
المؤلف:
Spanier, J. and Oldham, K. B
المصدر:
An Atlas of Functions. Washington, DC: Hemisphere
الجزء والصفحة:
...
25-5-2019
2238
Sawtooth Wave
The sawtooth wave, called the "castle rim function" by Trott (2004, p. 228), is the periodic function given by
 |
(1)
|
where 
is the fractional part 
, 
is the amplitude, 
is the period of the wave, and 
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 
, 
, and 
, then the Fourier series is given by
 |
(2)
|
and the function can be written
where 
is the floor function.
REFERENCES:
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. http://www.mathematicaguidebooks.org/.
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