对于实数或者整数函数来说,周期性意味着按照一定的间隔重复一个特定部分就可以绘制出完整的函数图。如果在函数 f 中所有的位置 x 都满足
那幺,f 就是周期为 T 的周期函数。非周期函数就是没有类似周期 T 的函数。
如果周期函数 f 的周期为 T,那幺对于 f 中的任意 x 以及任意整数 n,有
在上面的例子中,P 是 1, f( x ) = f( x + 1 ) = f( x + 2 ) = ...。但是函数周期不一定是满足上述等式的最小值,T 也可以是 2。
英语百科
Periodic function 周期函数
(重定向自Periodic signal)
"Aperiodic" and "Non-periodic" redirect here. For other uses, see Aperiodic (disambiguation).
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of 2π radians. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function which is not periodic is called aperiodic.