A Fourier series is a continuous, periodic function created by a summation of harmonically related sinusoidal functions. It has several different, but equivalent, forms, shown here … See more

The Fourier series is named in honor of Jean-Baptiste Joseph Fourier (1768–1830), who made important contributions to the study of trigonometric series, … See more

When the real and imaginary parts of a complex function are decomposed into their even and odd parts, there are four components, denoted below by the subscripts RE, RO, IE, and IO. And there is a one-to-one mapping between the four components of a … See more

Fourier series on a square
We can also define the Fourier series for functions of two variables $${\displaystyle x}$$ and $${\displaystyle y}$$ in the square
Aside from being … See more

This table shows some mathematical operations in the time domain and the corresponding effect in the Fourier series coefficients. Notation:
• Complex conjugation is denoted by an asterisk.
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Riemann–Lebesgue lemma
If $${\displaystyle S}$$ is integrable, $${\textstyle \lim _{|n|\to \infty }S[n]=0}$$, See more

These theorems, and informal variations of them that don't specify the convergence conditions, are sometimes referred to generically as Fourier's theorem or the Fourier theorem. See more