A function f is said to be periodic if, for some nonzero constant P, it is the case that
$${\displaystyle f(x+P)=f(x)}$$
for all values of x in … See more

Periodic functions can take on values many times. More specifically, if a function $${\displaystyle f}$$ is periodic with period $${\displaystyle P}$$, then for all $${\displaystyle x}$$ in … See more

Consider a real waveform consisting of superimposed frequencies, expressed in a set as ratios to a fundamental frequency, f: F = 1⁄f [f1 f2 f3 ... fN] … See more

• "Periodic function". Encyclopedia of Mathematics. EMS Press. 2001 [1994].
• Weisstein, Eric W. "Periodic Function". MathWorld. See more

Real number examples
The sine function is periodic with period $${\displaystyle 2\pi }$$, since
$${\displaystyle \sin(x+2\pi )=\sin x}$$
for all values of $${\displaystyle x}$$. This function repeats on intervals of length
Everyday examples … See more

Antiperiodic functions
One subset of periodic functions is that of antiperiodic functions. This is a function $${\displaystyle f}$$ such … See more

• Almost periodic function
• Amplitude
• Continuous wave
• See more