有关1/3倍频程的讨论

huaijuliu

将全频域按几何等比级数的间隔划分，使得中心频率fc取做带宽上、下限f1、f2的几何平均值，且带宽h＝f2－f1 总是和中心频率fc保持一常数关系，h＝v×fc。如果v等于根号二的倒数（0.707)，那么f2＝2f1，则定义这样的频率带宽叫倍频程带宽；如果v等于三倍根号二的倒数（0.236），那么h＝0.236fc，则定义这样的频率带宽为1/3倍频程带宽。

1/3倍频程作用主要是分析噪声能量的频率分布。另外做分析的时候加了计权网络可起到滤波功能。

每个倍频程或者1/3倍频程的获得是通过带通滤波实现的。但是作为总的倍频程或者1/3倍频程分析来看，主要是为了研究信号能量在不同频带的分布。

使用1/3倍频程主要是因为人耳对声音的感觉，其频率分辨能力不是单一频率，而是频带，而1/3倍频程曾经被认为是比较符合人耳特性的频带划分方法，不过现在心理声学里提出了Critical Band这么个频带划分方法，听说更符合人耳特性。

先要知道1/3倍频程的划分方法，相关的书和国标都有公式和现成的数据表格，然后，你将时间域的声信号fft变换到频率域，对定义的每个1/3倍频带的声压计算等效连续声压级。这就是1/3倍频程声压级。

FFT后再进行1/3倍频程分析，在王济和胡晓编“MATLAB在振动信号处理中的应用”（中国水利水电出版社）一书中有一节用介绍1/3倍频程分析，它是在FFT之后用1/3倍频程滤波器对信号进行分析处理，求出1/3倍频程滤波器输出的均方根值，并提供了MATLAB程序。

Spectrum analysis using filters whose bandwidth is a fractional ratio of the center frequency of the filter. For example, a 1/3 octave filter centered at 1000 Hz would have a bandwidth of 260 Hz (26% equals 1/3 octave). Bandwidth (relative to a normalized center frequency of 1) is computed as 2(1/N)-1. The typical bandwidths used (primarily for acoustical and vibration ananlysis) are 1/1 octave, 1/3, 1/12, and 1/24 octave.

Octave band filters do not have infinitely steep skirts. Therefore, an isolated tone may produce a reading in adjacent octave bands. Also, a tone at the nominal boundary between two bands produces an equal reading in both. (For example, a 60 dB tone at 707.1 Hz would give readings of 57 dB each in the 500 Hz and 1000 Hz octave bands.) Note also that filters designed according to ANSI S1.11 and IEC 1260 filters have different skirts. Bands adjacent to a strong tone may have different numerical readings with the two types of filters. The actual filter band center frequencies are typically developed as a series of powers of 21/3 times 1000 Hz, and therefore, may not correspond precisely to the nominal band center frequencies.

1/N octave filters have a constant relative bandwidth, which means that the Q factor of the filters are the same. In many respects, this is similar to many natural systems, which tend to have a similar behavior and are best viewed on a logarithmic frequency axis. For example, the frequency response of a simple (first order) low-pass filter looks like a straight line when plotted on a logarithmic frequency axis.

The following is a table of octave and third-octave filter center frequencies:

huaijuliu

Table below summarized the octave and the 1/3 octave middle frequencies and bands computed from expressions reported in the table above.

huaijuliu

The figure represents the conversion from narrow frequency bands within the range [200-4000] Hz to one-third octave frequency bands for the sound absorption coefficient of a 30 mm-thick fibrous纤维的 material measured at normal incidence法线入射 in a standing wave tube.
The values of the sound absorption coefficient included in a 1/3 octave band are averaged平均; the obtained mean value of the sound absorption coefficient is then reported at the 1/3 octave middle frequency.

ChaChing

谢谢楼主辛苦的整理!
但是分散了好几层楼, 读来总觉不方便!
若能整成一电子档, 方便别人下载学习, 亦不会让人误以为灌水!

taqing

1/3倍频程在振动加速度时有什么好处？

sdjxmx

知识呀！补习一下，多谢

huaijuliu

频带：把宽广的声音频率变化范围划分为若干较小的段落，叫做频带(频程)。任一频带都有上限频率 、下限频率 (这两个频率又称截至频率)和中心频率，上、下限频率之间的频率范围称为频带宽度，又称带宽。

　　倍频带(倍频程)：如果两个频率相差一倍，称这两个频率之间相差一个倍频带。上限频率 、下限频率和倍频带系数n有确定关系。
振动位移在研究机械结构强度和变形时有意义;加速度在研究机械疲劳、冲击和评价振动对人的影响时有重要意义;振动速度和结构辐射噪声大小有关联。

art0721

学习一下，谢谢楼主，辛苦～

luningxia

:@L 是幽默么，还是。。。
1/3倍频程一般不用在这的 估计也没有人用

pittsun

太好了，正好想学习一下1/3倍频。

zzxiayong

很好，很强大

guof_

谢谢了！！

山東男孩

非常精闢啊 謝謝分享

aoyanling

1/N octave filters have a constant relative bandwidth, which means that the Q factor of the filters are the same. In many respects, this is similar to many natural systems, which tend to have a similar behavior and are best viewed on a logarithmic frequency axis. For example, the frequency response of a simple (first order) low-pass filter looks like a straight line when plotted on a logarithmic frequency axis.  

楼主上面红色字体的怎么翻译啊？请教了！多谢！

superxjw

好贴，不要沉了！