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rectangular function : ウィキペディア英語版
rectangular function

The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as:
:\mathrm(t) = \Pi(t) = \begin
0 & \mbox |t| > \frac \\
\frac & \mbox |t| = \frac \\
1 & \mbox |t| < \frac. \\
\end
Alternative definitions of the function define \mathrm(\pm \tfrac) to be 0, 1, or undefined.
==Relation to the boxcar function==
The rectangular function is a special case of the more general boxcar function:
:\operatorname\left(\frac \right) = u(t - (X - Y/2)) - u(t - (X + Y/2)) = u(t - X + Y/2) - u(t - X - Y/2)
Where u is the Heaviside function; the function is centered at X and has duration Y, from X-Y/2 to X+Y/2.
Another example is this:
rect((t - (T/2)) / T ) goes from 0 to T, so in terms of Heaviside function u(t) - u((t-T) / T )

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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