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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 doubly periodic function is thus a two-dimensional extension of the simpler singly periodic function, which repeats itself in a single dimension. Familiar examples of functions with a single period on the real number line include the trigonometric functions like cosine and sine , In the complex plane the exponential function e z is a singly ...
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 ...
The Fourier transform of a periodic function cannot be defined using the integral formula directly. In order for integral in Eq.1 to be defined the function must be absolutely integrable. Instead it is common to use Fourier series. It is possible to extend the definition to include periodic functions by viewing them as tempered distributions.
The kernel functions are periodic with period . Plot restricted to one period [ − L , L ] , L = π , {\displaystyle [-L,L],~L=\pi ,~} of the first few Dirichlet kernels showing their convergence to one of the Dirac delta distributions of the Dirac comb .