MATLAB实现倍频程
如何在MATLAB实现倍频程？ 倍频程是声学里人的可听频率范围内，将声音的频谱进行一定规则的集中，变成有限的几个频点对应的强度，这样描述比较起来容易，是一种公约的描述形式。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，但1/3倍频程仍在广泛使用。分析频谱时，对于连续谱而言，分析某频率点上的声功率是没有意义的，因此有必要统计某一频带内的声功率。对于频带划分，倍频程和1/3倍频程是常用的划分方法之一，它们都是相对恒定带宽，例如1/3倍频程的带宽是中心频率的23%。声学及振动测量仪器中的倍频程及1/3倍频程滤波主要是用于对噪声或振动进行频谱分析用的,它们是一种等百分比带宽滤波器,与人耳的频谱分析特性相似。在噪声测量中，使用1/3oct主要是将噪声的频率分布情况更直观的表示出来。便于今后的工作开展。百分比=(2^(m/2)-2^(-m/2))*100%其中m就是几倍频程，1/3倍频程m等于1/3。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，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。 function = oct3spec(B,A,Fs,Fc,s,n);% OCT3SPEC Plots a one-third-octave filter characteristics.
% OCT3SPEC(B,A,Fs,Fc) plots the attenuation of the filter defined by
% B and A at sampling frequency Fs. Fc is the center frequency of
% the one-third-octave filter. The plot covers one decade on both sides
% of Fc.
%
% OCT3SPEC(B,A,Fs,Fc,'ANSI',N) superposes the ANSI Order-N analog
% specification for comparison. Default is N = 3.
%
% OCT3SPEC(B,A,Fs,Fc,'IEC',N) superposes the characteristics of the
% IEC 61260 class N specification for comparison. Default is N = 1.
%
% = OCT3SPEC(B,A,Fs,Fc) returns two 512-point vectors with
% the gain (in dB) in G and logarithmically spaced frequencies in F.
% The plot can then be obtained by SEMILOGX(F,G)
%
% See also OCT3DSGN, OCTSPEC, OCTDSGN.
% Author: Christophe Couvreur, Faculte Polytechnique de Mons ( Belgium)
% Last modification: Sept. 4, 1997, 11:00am.
% References:
% ANSI S1.1-1986 (ASA 65-1986): Specifications for
% Octave-Band and Fractional-Octave-Band Analog and
% Digital Filters, 1993.
% IEC 61260 (1995-08):Electroacoustics -- Octave-Band and
% Fractional-Octave-Band Filters, 1995.
if (nargin < 4) | (nargin > 6)
error('Invalide number of input arguments.');
end
ansi = 0;
iec = 0;
if nargin > 4
if strcmp(lower(s),'ansi')
ansi = 1;
if nargin == 5
n = 3;
end
elseif strcmp(lower(s),'cei') | strcmp(lower(s),'iec')
iec = 1;
if nargin == 5
n = 1
end
if (n < 0) | (n > 3)
error('IEC class must be 0, 1, or 2');
end
end
end
N = 512;
pi = 3.14159265358979;
F = logspace(log10(Fc/10),log10(min(Fc*10,Fs/2)),N);
H = freqz(B,A,2*pi*F/Fs);
G = 20*log10(abs(H));
% Set output variables
if nargout ~= 0
g = G; f = F;
return
end
% Generate the plot
if (ansi) % ANSI Order-n specification
f = logspace(log10(Fc/10),log10(Fc*10),N);
f1 = Fc/(2^(1/6));
f2 = Fc*(2^(1/6));
Qr = Fc/(f2-f1);
Qd = (pi/2/n)/(sin(pi/2/n))*Qr;
Af = 10*log10(1+Qd^(2*n)*((f/Fc)-(Fc./f)).^(2*n));
semilogx(F,G,f,-Af,'--');
legend('Filter',['ANSI order-' int2str(n)],0);
elseif (iec) % CEI specification
semilogx(F,G);
hold on
if n == 0
tolup =[ .15 .15 .15 .15 .15 -2.3 -18.0 -42.5 -62 -75 -75 ];
tollow = [ -.15 -.2 -.4 -1.1 -4.5 -realmax -inf -inf -inf -inf -inf ];
elseif n == 1
tolup =[ .3 .3 .3 .3 .3 -2 -17.5 -42 -61 -70 -70 ];
tollow = [ -.3 -.4 -.6 -1.3 -5 -realmax -inf -inf -inf -inf -inf ];
elseif n == 2
tolup =[ .5 .5 .5 .5 .5 -1.6 -16.5 -41 -55 -60 -60];
tollow = [ -.5 -.6 -.8 -1.6 -5.5 -realmax -inf -inf -inf -inf -inf ];
end
% Reference frequencies in base 2 system
f = Fc * [1 1.02676 1.05594 1.08776 1.12246 1.12246 1.29565 1.88695 ...
3.06955 5.43474 NaN ];
f(length(f)) = realmax;
ff = Fc * [1 0.97394 0.94702 0.91932 0.89090 0.89090 0.77181 0.52996 ...
0.32578 0.18400 NaN ];
ff(length(ff)) = realmin;
semilogx(F,G,f,tolup,'--');
semilogx(F,G,f,tollow,'--');
semilogx(F,G,ff,tolup,'--');
semilogx(F,G,ff,tollow,'--');
hold off
legend('Filter',['IEC class ' int2str(n)],0);
else
semilogx(F,G);
end
xlabel('Frequency '); ylabel('Gain ');
title(['One-third-octave filter: Fc =',int2str(Fc),' Hz, Fs = ',int2str(Fs),' Hz']);
axis();
grid on
function = oct3dsgn(Fc,Fs,N);
% OCT3DSGNDesign of a one-third-octave filter.
% = OCT3DSGN(Fc,Fs,N) designs a digital 1/3-octave filter with
% center frequency Fc for sampling frequency Fs.
% The filter is designed according to the Order-N specification
% of the ANSI S1.1-1986 standard. Default value for N is 3.
% Warning: for meaningful design results, center frequency used
% should preferably be in range Fs/200 < Fc < Fs/5.
% Usage of the filter: Y = FILTER(B,A,X).
%
% Requires the Signal Processing Toolbox.
%
% See also OCT3SPEC, OCTDSGN, OCTSPEC.
% Author: Christophe Couvreur, Faculte Polytechnique de Mons (Belgium)
% Last modification: Aug. 25, 1997, 2:00pm.
% References:
% ANSI S1.1-1986 (ASA 65-1986): Specifications for
% Octave-Band and Fractional-Octave-Band Analog and
% Digital Filters, 1993.
if (nargin > 3) | (nargin < 2)
error('Invalide number of arguments.');
end
if (nargin == 2)
N = 3;
end
if (Fc > 0.88*(Fs/2))
error('Design not possible. Check frequencies.');
end
% Design Butterworth 2Nth-order one-third-octave filter
% Note: BUTTER is based on a bilinear transformation, as suggested in .
pi = 3.14159265358979;
f1 = Fc/(2^(1/6));
f2 = Fc*(2^(1/6));
Qr = Fc/(f2-f1);
Qd = (pi/2/N)/(sin(pi/2/N))*Qr;
alpha = (1 + sqrt(1+4*Qd^2))/2/Qd;
W1 = Fc/(Fs/2)/alpha;
W2 = Fc/(Fs/2)*alpha;
= butter(N,);
function = oct3bank(x);
% OCT3BANK Simple one-third-octave filter bank.
% OCT3BANK(X) plots one-third-octave power spectra of signal vector X.
% Implementation based on ANSI S1.11-1986 Order-3 filters.
% Sampling frequency Fs = 44100 Hz. Restricted one-third-octave-band
% range (from 100 Hz to 5000 Hz). RMS power is computed in each band
% and expressed in dB with 1 as reference level.
%
% = OCT3BANK(X) returns two length-18 row-vectors with
% the RMS power (in dB) in P and the corresponding preferred labeling
% frequencies (ANSI S1.6-1984) in F.
%
% See also OCT3DSGN, OCT3SPEC, OCTDSGN, OCTSPEC.
% Author: Christophe Couvreur, Faculte Polytechnique
matlab进行内插----就是在一组数种插入0
比如以前数组为A=
现在可以内插后就编程A=,如果这个是时域的变化，时域扩大3倍，根据傅里叶变换性质就知道，频域缩小成原来的1/3，幅度也是原来的1/3，内插补零以后，经过fft，就可以达到1/3倍频，只需要再乘以系数3，就可以了
抽取---就是隔几个抽取一次
在频域中进行抽取也可以。
比如A=
只需要编写n=1:(size(1)/3) B(n)=A(3*n),直接在频域进行抽取可以满足LZ的要求，B=
好东西啊，谢谢各位大神~~~~ 怪咖先生 发表于 2016-10-10 09:06
matlab进行内插----就是在一组数种插入0
比如以前数组为A=
现在可以内插后就编程A=
这就是传说中的补零吗 Eminem 发表于 2016-10-8 13:34
倍频程是声学里人的可听频率范围内，将声音的频谱进行一定规则的集中，变成有限的几个频点对应的强度，这样 ...
谢谢{:{39}:} Eminem 发表于 2016-10-8 13:34
倍频程是声学里人的可听频率范围内，将声音的频谱进行一定规则的集中，变成有限的几个频点对应的强度，这样 ...
试试看看好使不感谢分享
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