倍频程与十倍频程.doc

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:国外倍频程计算.JPG (44.3 KB, 下载次数: 57) 2009-10-13 20:53 上传下载次数: 57Table below summarized the octave and the 1/3 octave middle frequencies and bands computed from expressions reported in the table above.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.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倍频程与十倍频程lugiwin 发表于 - 2007-9-29 10:08:0010推荐昨日在看分频器的资料，第一次看到一阶（6db/oct），二阶（12db/oct）和三阶（18db/oct）的提法，也是对滤波器来说的可上学时没听说过这个提法啊，一直就是一阶滤波器的衰减是-20dB/十倍频程,二阶滤波器的衰减是-40dB/十倍频程所以网上搜了一下，学习！-----------------------------------------------------------------------------------------------------------------decade(十倍频程);octave(倍频程) 2倍频和10倍频是一回事对于滤波或运放放大倍数来讲是用dB来表示的。

具体的公式是  A(w)=A0/(1+jw/w0), w0是滤波频率或运放的一个极点  采用dB表示时是      20*log|A(w)|.      A(w)要取模，即A0/sqrt(1+w*w/(w0*w0)).对于n倍频(靠近w0的频率不准确,n>0),w2=n*w1, w1>>w0.(开方中的1可忽略)则有       A(w2)-A(w1)=20*logA0-20*log(sqrt(w2*w2)/(w0*w0))                   -20*logA0+20*log(sqrt(w1*w1)/(w0*w0))                  =-10*log(w2*w2/(w1*w1)                  =-10*log(n*n)这样对于两倍频，w2=2*w1,则此时下降是         -10*log4=-6.02dB当w2=10*w1时         -10*log100=-20dB.。