Fourier transform polynomial

Fourier trigonometric series {Fourier transform, function} can represent function over interval.

transformation

Function can transform by multiplying function by periodic function and integrating. Integral from x = -infinity to x = +infinity of g(x) * e^(-i * 2 * pi * u * x) * dx, where x = domain value, g(x) is function, u is frequency, and i is square root of -1.

transformation: coordinates

Fourier trigonometric series can transform coordinates. (1/(2 * pi)) * (integral from q = -infinity to q = +infinity of (e^(i*q*x)) * dq) * (integral from a = -infinity to a = +infinity of F(a) * (e^(-i*q*x)) * da).

limit

Fourier series go to limit as period approaches infinity.

time

Time t relates to phase A: t = tan(A/2).

power series

Complex power series can represent periodic functions with holomorphic positive and negative frequency.

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3-Algebra-Function-Kinds-Trigonometric

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Date Modified: 2022.0224