查看“︁倍频程”︁的源代码

{{onesource|time=2019-04-03T06:17:46+00:00}}
'''倍频程'''（{{lang-en|octave band}}），又称为'''倍频带'''，是振动与噪音分析中将整个[[频谱]]划分为若干[[频带]]的方法，每个频带的上限频率是下限频率的两倍。类似地，1/3倍频程（one-third octave band）指每个频带的上限频率与下限频率之比是2的[[立方根]]。

== 倍频程 ==
=== 计算 ===
假设每个频带的中心频率为<math>f_c</math>，该频带的上限频率与下限频率可由下式计算：

:<math>f_c = \sqrt{2} f_{min} = \frac{f_{max}}{\sqrt{2}}</math>,

其中<math>f_{min}</math>为下限频率，<math>f_{max}</math>为上限频率。

=== 名称 ===
{| class="wikitable"
|-
! 频带序号 !! 标称频率<ref>{{cite web|title=ANSI S1.11: Specification for Octave, Half-Octave, and Third Octave Band Filter Sets|url=https://law.resource.org/pub/us/cfr/ibr/002/ansi.s1.11.2004.pdf|accessdate=7 March 2018|archive-date=2020-10-25|archive-url=https://web.archive.org/web/20201025223931/https://law.resource.org/pub/us/cfr/ibr/002/ansi.s1.11.2004.pdf|dead-url=no}}</ref> !! 计算频率 !! A计权修正
|-
| -1 || 16&nbsp;Hz || 15.625&nbsp;Hz || 
|-
| 0 || 31.5&nbsp;Hz || 31.250&nbsp;Hz || -39.4&nbsp;dB
|-
| 1 || 63&nbsp;Hz || 62.500&nbsp;Hz || -26.2&nbsp;dB
|-
| 2 || 125&nbsp;Hz || 125.000&nbsp;Hz || -16.1&nbsp;dB
|-
| 3 || 250&nbsp;Hz || 250.000&nbsp;Hz || -8.6&nbsp;dB
|-
| 4 || 500&nbsp;Hz || 500.000&nbsp;Hz || -3.2&nbsp;dB
|-
| 5 || 1k Hz || 1000.000&nbsp;Hz || 0&nbsp;dB
|-
| 6 || 2k Hz || 2000.000&nbsp;Hz || 1.2&nbsp;dB
|-
| 7 || 4k Hz || 4000.000&nbsp;Hz || 1&nbsp;dB
|-
| 8 || 8k Hz || 8000.000&nbsp;Hz || -1.1&nbsp;dB
|-
| 9 || 16k Hz || 16000.000&nbsp;Hz || -6.6&nbsp;dB
|}

== 1/3倍频程 ==
=== 以2为基数 ===

<syntaxhighlight lang="matlab">
%% Calculate Third Octave Bands (base 2) in Matlab
fcentre  = 10^3 * (2 .^ ([-18:13]/3))
fd = 2^(1/6);
fupper = fcentre * fd
flower = fcentre / fd
</syntaxhighlight>

=== 为10为基数 ===

<syntaxhighlight lang="matlab">
%% Calculate Third Octave Bands (base 10) in Matlab
fcentre = 10.^(0.1.*[12:43])
fd = 10^0.05;
fupper = fcentre * fd
flower = fcentre / fd
</syntaxhighlight>

===名称===

{| class="wikitable"
! 频带序号 || 标称频率 || 计算频率（以2为基数） || 计算频率（以10为基数）
|-
| 1 || 16&nbsp;Hz || 15.625&nbsp;Hz || 15.849&nbsp;Hz
|-
| 2 || 20&nbsp;Hz || 19.686&nbsp;Hz || 19.953&nbsp;Hz
|-
| 3 || 25&nbsp;Hz || 24.803&nbsp;Hz || 25.119&nbsp;Hz
|-
| 4 || 31.5&nbsp;Hz || 31.250&nbsp;Hz || 31.623&nbsp;Hz
|-
| 5 || 40&nbsp;Hz || 39.373&nbsp;Hz || 39.811&nbsp;Hz
|-
| 6 || 50&nbsp;Hz || 49.606&nbsp;Hz || 50.119&nbsp;Hz
|-
| 7 || 63&nbsp;Hz || 62.500&nbsp;Hz || 63.096&nbsp;Hz
|-
| 8 || 80&nbsp;Hz || 78.745&nbsp;Hz || 79.433&nbsp;Hz
|-
| 9 || 100&nbsp;Hz || 99.213&nbsp;Hz || 100&nbsp;Hz
|-
| 10 || 125&nbsp;Hz || 125.000&nbsp;Hz || 125.89&nbsp;Hz
|-
| 11 || 160&nbsp;Hz || 157.490&nbsp;Hz || 158.49&nbsp;Hz
|-
| 12 || 200&nbsp;Hz || 198.425&nbsp;Hz || 199.53&nbsp;Hz
|-
| 13 || 250&nbsp;Hz || 250.000&nbsp;Hz || 251.19&nbsp;Hz
|-
| 14 || 315&nbsp;Hz || 314.980&nbsp;Hz || 316.23&nbsp;Hz
|-
| 15 || 400&nbsp;Hz || 396.850&nbsp;Hz || 398.11&nbsp;Hz
|-
| 16 || 500&nbsp;Hz || 500.000&nbsp;Hz || 501.19&nbsp;Hz
|-
| 17 || 630&nbsp;Hz || 629.961&nbsp;Hz || 630.96&nbsp;Hz
|-
| 18 || 800&nbsp;Hz || 793.701&nbsp;Hz || 794.33&nbsp;Hz
|-
| 19 || 1&nbsp;kHz || 1000.000&nbsp;Hz || 1000&nbsp;Hz
|-
| 20 || 1.25&nbsp;kHz || 1259.921&nbsp;Hz || 1258.9&nbsp;Hz
|-
| 21 || 1.6&nbsp;kHz || 1587.401&nbsp;Hz || 1584.9&nbsp;Hz
|-
| 22 || 2&nbsp;kHz || 2000.000&nbsp;Hz || 1995.3&nbsp;Hz
|-
| 23 || 2.5&nbsp;kHz || 2519.842&nbsp;Hz || 2511.9&nbsp;Hz
|-
| 24 || 3.150&nbsp;kHz || 3174.802&nbsp;Hz || 3162.3&nbsp;Hz
|-
| 25 || 4&nbsp;kHz || 4000.000&nbsp;Hz || 3981.1&nbsp;Hz
|-
| 26 || 5&nbsp;kHz || 5039.684&nbsp;Hz || 5011.9&nbsp;Hz
|-
| 27 || 6.3&nbsp;kHz || 6349.604&nbsp;Hz || 6309.6&nbsp;Hz
|-
| 28 || 8&nbsp;kHz || 8000.000&nbsp;Hz || 7943.3&nbsp;Hz
|-
| 29 || 10&nbsp;kHz || 10079.368&nbsp;Hz || 10&nbsp;kHz
|-
| 30 || 12.5&nbsp;kHz || 12699.208&nbsp;Hz || 12.589&nbsp;kHz
|-
| 31 || 16&nbsp;kHz || 16000.000&nbsp;Hz || 15.849&nbsp;kHz
|-
| 32 || 20&nbsp;kHz || 20158.737&nbsp;Hz || 19.953&nbsp;kHz
|}

== 参考文献 ==
{{reflist}}

[[Category:声学]]