查看“︁锯齿波”︁的源代码

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{{expert|time=2019-09-08T11:36:22+00:00}}
[[Image:Synthesis sawtooth.gif|thumb|350px|right|大量谐波叠加生成锯齿波的过程动画演示。对于该过程的数学描述，请参阅[[傅里叶变换]]。]]
'''锯齿波'''（{{lang-en|'''sawtooth wave'''}}）是一种非[[正弦曲线|正弦]]波，由于它具有类似[[锯子]]一样的[[波形]]，即具有一条直的斜线和一条垂直于横轴的直线的重复结构，它被命名为锯齿波。

鋸齒波的[[傅里葉級數]]展開為：
: <math>x_\mathrm{sawtooth}(t) = \frac {2}{\pi}\sum_{k=1}^{\infty} {(-1)}^{k} \frac {\sin (2\pi kft)}{k} </math>

== 相关条目 ==
{{Listen|filename=Sawtooth-aliasingdemo.ogg|title=Sawtooth aliasing demo|description=Sawtooth waves played bandlimited and aliased at 440&nbsp;Hz, 880&nbsp;Hz, and 1760&nbsp;Hz |format=[[Ogg]]}}
[[Image:Waveforms.svg|thumb|400px|[[正弦曲线|正弦波]]、[[方波]]、[[三角波]]和锯齿波的[[波形]]]]
*[[方波]]
*[[三角波]]

== 参考文献 ==
{{reflist}}
*{{cite book | author=Hugh L. Montgomery | authorlink=Hugh Montgomery (mathematician) | coauthors=[[Robert Charles Vaughan (mathematician)|Robert C. Vaughan]] | title=Multiplicative number theory I. Classical theory | series=Cambridge tracts in advanced mathematics | volume=97 | year=2007 | isbn=0-521-84903-9 | pages=536–537}}

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