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Raised-cosine filter : ウィキペディア英語版
Raised-cosine filter
The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation due to its ability to minimise intersymbol interference (ISI). Its name stems from the fact that the non-zero portion of the frequency spectrum of its simplest form (\beta = 1) is a cosine function, 'raised' up to sit above the f (horizontal) axis.
==Mathematical description==

The raised-cosine filter is an implementation of a low-pass Nyquist filter, i.e., one that has the property of vestigial symmetry. This means that its spectrum exhibits odd symmetry about \frac, where T is the symbol-period of the communications system.
Its frequency-domain description is a piecewise function, given by:
:H(f) = \begin
T,
& |f| \leq \frac \\
\frac\left,
& \frac < |f| \leq \frac \\
0,
& \mbox
\end
or in terms of havercosines:
:H(f) = \begin
T,
& |f| \leq \frac \\
T\operatorname\left(\frac\left(- \frac\right )\right),
& \frac < |f| \leq \frac \\
0,
& \mbox
\end
for
:0 \leq \beta \leq 1

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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