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Octave (electronics)
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Octave (electronics) : ウィキペディア英語版
Octave (electronics)
In electronics, an octave is a doubling or halving of a frequency. The term is derived from the Western musical scale (an octave is a doubling in frequency) and is therefore common in audio electronics. (The prefix octa-, denoting eight, refers to the eight notes of a diatonic scale.) Along with the decade, it is a unit used to describe frequency bands or frequency ratios.〔Levine, William S. (2010). ''The Control Handbook: Control System Fundamentals'', p.9-29. ISBN 9781420073621/ISBN 9781420073669.〕〔Perdikaris, G. (1991). ''Computer Controlled Systems: Theory and Applications'', p.117. ISBN 9780792314226.〕
A frequency ratio expressed in octaves is the base-2 logarithm (binary logarithm) of the ratio:
: \mathrm = \log_2\left(\frac\right)
An amplifier or filter may be stated to have a frequency response of ±6dB per octave over a particular frequency range, which signifies that the power gain changes by ±6 decibels (a factor of 4 in power), when the frequency changes by a factor of 2. This slope, or more precisely 10\log_(4) \approx 6.0206 decibels per octave, corresponds to an amplitude gain proportional to frequency, which is equivalent to ±20dB per decade (factor of 10 amplitude gain change for a factor of 10 frequency change). This would be a first-order filter.
==Example==
1. The distance between the frequencies 20 Hz and 40 Hz is 1 octave.
2. An amplitude of 52 dB at 4 kHz decreases as frequency increases at −2 dB/octave. What is the amplitude at 13 kHz?
: \text = \log_2\left(\frac\right) = 1.7
: \text_ + (1.7\text \times -2\text) = 48.6\text.\,

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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