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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Decade (log scale) ： ウィキペディア英語版 Decade (log scale) One decade is a factor of 10 difference between two numbers (an order of magnitude difference) measured on a logarithmic scale. Along with the octave, it is a logarithmic unit used to describe frequency bands or frequency ratios.〔Levine, William S. (2010). ''The Control Handbook: Control System Fundamentals'', p.9-29. ISBN 9781420073621.〕〔Perdikaris, G. (1991). ''Computer Controlled Systems: Theory and Applications'', p.117. ISBN 9780792314226.〕 It is especially useful when referring to frequencies and when describing frequency response of electronic systems, such as audio amplifiers and filters. ==Calculations== The factor-of-ten in a decade can be in either direction: so one decade up from 100 Hz is 1000 Hz, and one decade down is 10 Hz. The factor-of-ten is what is important, not the unit used, so 3.14 rad/s is one decade down from 31.4 rad/s. To determine the number of decades between two frequencies ($f\_1$ & $f\_2$), use the logarithm of the ratio of the two values: *$\backslash log\_\; (f\_2/f\_1)\backslash over\backslash log\_\; (10)$ decades〔〔 or, using natural logarithms: *$\backslash ln\; f\_2\; -\; \backslash ln\; f\_1\backslash over\backslash ln\; 10$ decades〔Davis, Don and Patronis, Eugene (2012). ''Sound System Engineering'', p.13. ISBN 9780240808307.〕 :How many decades is it from 15 rad/s to 150,000 rad/s? ::$\backslash log\_\; (150000/15)\; =\; 4$ decades :How many decades is it from 3.2 GHz to 4.7 MHz? ::$\backslash log\_\; (4.7\backslash times10^6\; /\; 3.2\backslash times10^9\; )\; =\; -2.83$ decades :How many decades is one octave? ::One octave is a factor of 2, so $\backslash log\_\; (2)\; =\; 0.301$ decades per octave (decade = just major third + three octaves, 10/1 = 5/4) To find out what frequency is a certain number of decades from the original frequency, multiply by appropriate powers of 10: :What is 3 decades down from 220 Hz? ::$220\; \backslash times\; 10^\; =\; 0.22$ Hz :What is 1.5 decades up from 10? ::$10\; \backslash times\; 10^\; =\; 316.23$ To find out the size of a step for a certain number of frequencies per decade, raise 10 to the power of the inverse of the number of steps: :What is the step size for 30 steps per decade? ::$10^\; =\; 1.079775$ - or each step is 7.9775% larger than the last. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Decade (log scale)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.