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This is a list of some well-known periodic functions. The constant function f ( x ) = c , where c is independent of x , is periodic with any period, but lacks a fundamental period . A definition is given for some of the following functions, though each function may have many equivalent definitions.
A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle . [ 1 ]
Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials. Natural logarithm; Common logarithm; Binary logarithm; Power functions: raise a variable number to a fixed power; also known as Allometric functions; note: if the power is a rational number it is not strictly a transcendental function. Periodic ...
Periodic function; List of periodic functions; Pfaffian function; Piecewise linear function; Piecewise property; Polyconvex function; Positive-definite function; Positive-real function; Progressive function; Proper convex function; Proto-value function; Pseudoanalytic function; Pseudoconvex function
The Fourier series of a periodic even function includes only cosine terms. The Fourier series of a periodic odd function includes only sine terms. The Fourier transform of a purely real-valued even function is real and even. (see Fourier analysis § Symmetry properties) The Fourier transform of a purely real-valued odd function is imaginary and ...
This is a list of recurring cycles. See also ... Almost periodic function – Amplitude modulation – Amplitude – Beat – Chaos theory – Cyclic group ...
Holomorphic function: complex-valued function of a complex variable which is differentiable at every point in its domain. Meromorphic function: complex-valued function that is holomorphic everywhere, apart from at isolated points where there are poles. Entire function: A holomorphic function whose domain is the entire complex plane.
The same discrete set is obtained by treating the duration of the segment as one period of a periodic function and computing the Fourier series coefficients. Sine and cosine transforms: When the input function has odd or even symmetry around the origin, the Fourier transform reduces to a sine transform or a cosine transform, respectively.