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Triangle wave
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Triangle wave : ウィキペディア英語版
Triangle wave

A triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function.
Like a square wave, the triangle wave contains only odd harmonics, demonstrating odd symmetry. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse).
==Harmonics==

It is possible to approximate a triangle wave with additive synthesis by adding odd harmonics of the fundamental, multiplying every (4n−1)th harmonic by −1 (or changing its phase by π), and rolling off the harmonics by the inverse square of their relative frequency to the fundamental.
This infinite Fourier series converges to the triangle wave with cycle frequency over time :
:\begin
x_\mathrm(t) & \sum_^\infty (-1)^k \, \frac \\
& \left( \sin (2\pi ft)- \sin (6\pi ft)+ \sin (10\pi ft) - \cdots \right)
\end

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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