Fourier Series
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Fourier Series
</dt>
The representation of a function f(x) in an interval
(-L, L) by a series consisting of sines and cosines with a
common period 2L, in the form,
Fourier coefficients are defined as
and
</p>
</dd>
'When f(x) is an even function, only the cosine terms appear; when f(x)
is odd, only the sine terms appear.
'</dd>
'The conditions on f(x) guaranteeing convergence of the series are quite
general, and the series may serve as a root-mean-square approximation even
when it does not converge.
'</dd>
'If the function is defined on an infinite interval and is not periodic, it
is represented by the Fourier integral. By either representation, the function
is decomposed into periodic components whose frequencies constitute the
spectrum of the function. The Fourier series employs a discrete spectrum of
wavelengths 2 L / n(n = 1,2,...); the Fourier integral requires
a continuous spectrum.
'</dd>
'See Fourier
transform. [[/a>|/a>
]]</dd>
References
This article is based on NASA's Dictionary of Technical Terms for Aerospace Use