An expansion of this type is known as a Fourier Series Expansion (Kreyszig, 1999, p. 530).

Note that each sinusoidal component has a frequency that is a multiple of the fundamental frequency, , and the radian fundamental frequency is .

There are two forms of the Fourier series: trigonometric and exponential. The form in Eq. (12.1) is called the trigonometric form.

The multiples of the fundamental frequency, f_{0}, are called harmonics of that fundamental frequency. The coefficients a_{0}, a_{n}, b_{n} are called the Fourier coefficients.

The Fourier coefficients are determined from the following formulas:

(12.2)

Note that a_{0} is the average value of x(t) over .

(12.3)

(12.4)

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