Hi jmebara,
The following is an example of a Bode diagram of the transfer function of a system, in which the 1/3 octave bands are highlighted:
Hi MF,
Good Point. Let me add some pics to see if I could make the question clearer.
According to one blog I visited why researching the following is described: "In Engineering applications, sound spectrums are usually represented in octave or one-third octave frequency bands rather than in narrow frequency bands. This frequency representation is linked to the perception of sound by a human ear and it allows a compression of the amount of information. An important part of the information is however lost when converting results from narrow frequency bands to octave or one-third octave frequency bands." The frequencies of the 1/3 Octave bands are as follows:
As an example on the blog, the following curve is shown which depicts the results of the conversion from narrow band to octave band with both curves plotted. In this example however, they are dealing with the sound absorption coefficient for a fibrous material. Also, Matlab was used:
% function [one_third_freq,band] = one_third_octave(frequencies,measurements)
%
% Narrow bands to one-third octave bands representation.
%
% Example: [one_third_freq_preferred,band] = narrow_to_one_third_octave(frequencies,alpha_diffuse)
%
% The input parameters are:
% o frequencies: frequency values
% (with a fixed of variable frequency step),
% o measurements: acoustic absorption coefficent values
% (corresponding to the frequency vector defined above).
%
% The output parameters are:
% o one_third_freq: center frequencies of 1/3 octave bands,
% o bands: values of the acoustic absorption coefficent in 1/3 bands
%
A plot which Shows what I am trying to get at can be seen in the following Picture which is an example of Sound pressure Level vs frequency (In the Picture, the narrowband is not depicted. It seems to have already been summed up or averaged to obtain the results in 1/3 Octave bands):
As you can see, the 1/3 Octave bands have been assessed and a smooth line plot has been created.
I would like to do something similar in Mathcad in which I get as final results the smooth line plot.
The following is a Matlab code to convert narrowband to 1/n octave band...These are some of the stuffs I have found while checking out how to do this whole Thing. I haven't personally tried out the following Matlab code. I will just be happy if I can do all this in Mathcad :):
%Program to convert narrowband data to 1/n octaveband data. Just send it an
%array of band center frequencies, the dB values to sort, and the nth
%octave band you want. This can be used with any dB values (e.g. Sound
%pressure level (SPL), sound power (Lw), sound intensity (Li), etc..
%
%Important Note 1: The given center frequencies must be a constant df apart
%
%Important Note 2: If your data was windowed during the FFT process and you
%used the amplitude correction factor (ACF), then you need to adjust your
%data to the energy correction factor when converting to octave spectra. See
%the first couple lines of the function to adjust this.
%
%-Examples:
%[sortedData,Fc,Flow,Fhigh] = NarrowToNthOctave([490,510,500],[60,60,60],1)
%[sortedData,Fc] = NarrowToNthOctave([490,510,500],[60,60,60],3)
%[sortedData,Fc] = NarrowToNthOctave(freqArray,dBArray,3)
%
%-V4 TMB 12/1/2015
function [sortedData,Fc,Flow,Fhigh] = NarrowToNthOctave(arrayOfNBCenterFreqs,arrayOfdBToConvert,n)
df=arrayOfNBCenterFreqs(2)-arrayOfNBCenterFreqs(1);
%Use correctionFactor=1 if you did not window or you used ECF
correctionFactor=1;
%Use this if you used a hanning window with ACF
% ACF=(1/mean(window(@hann,1028));
% ECF=(1/mean(window(@hann,1028));
% correctionFactor=ECF/ACF;
data=data*correctionFactor;
%Determine Initial Center frequency (Fc)
previous=1000*2^(1/n);
lowFc=1000; %Start at 1000 Hz and find lowest Fc
while (previous-lowFc) > df
previous=lowFc;
lowFc=lowFc/2^(1/n);
end
%Compute center frequencies
ii=1;
Fc(ii)=lowFc;
while Fc(ii) <= max(arrayOfNBCenterFreqs)
ii=ii+1;
Fc(ii)=2^(1/n)*Fc(ii-1);
end
%Compute high, low frequencies, and bandwidth (BW) from center frequencies
Flow=Fc/sqrt(2^(1/n));
Fhigh=Fc*sqrt(2^(1/n));
BW=Fhigh-Flow;
%Sort data in frequency bins
sortedData=zeros(1,length(Fc)); zeroFreqValue=0;
for jj=1:length(arrayOfdBToConvert) %Do for each value given
for kk=1:length(Fc) %Check each Fc bin to see where value should be placed
if arrayOfNBCenterFreqs(jj)>=Flow(kk) && arrayOfNBCenterFreqs(jj)<Fhigh(kk) %Find place. In the rare case a given center freq = flow(ii)/fhigh(ii+1) then sum the value in flow
if sortedData(kk)==0 %if no values has been added to the band then set initial value
sortedData(kk)=arrayOfdBToConvert(jj);
N(kk)=1;
else %else sum in the value
sortedData(kk)=10*log10(sum(10.^([sortedData(kk) arrayOfdBToConvert(jj)]./10))); %dB add value to that bin
N(kk)=N(kk)+1;
end
else %else check to see if the value belongs in the 0 Hz band
if (kk==1) && arrayOfNBCenterFreqs(jj)<Flow(kk)
if zeroFreqValue==0
zeroFreqValue=arrayOfdBToConvert(jj);
else
zeroFreqValue=10*log10(sum(10.^([zeroFreqValue arrayOfdBToConvert(jj)]./10))); %dB add value to that bin
end
end
end
end
end
%Apply bin correction factor for when center frequencies are not integer
%multiples of the bandwidth (BW)
for ll=1:length(N) %Look through each bin that had values added to it
if (N(ll)~=0) && (floor(BW(ll)/df)<=N(ll)) %If values were added and there are enough values added to make applying the correction appropriate then apply correction
sortedData(ll)=sortedData(ll)+10*log10(BW(ll)/(df*N(ll)));
end
end
%If DC value was given, add to sorted array
if zeroFreqValue~=0
sortedData=[zeroFreqValue sortedData];
Fc=[0 Fc];
Flow=[0 Flow];
Fhigh=[0 Fhigh];
end
%Remove unused bins at beginning if only higher freqs were given
removeThisMany=0;
for ll=1:length(sortedData)
if sortedData(ll)==0;
removeThisMany=1+removeThisMany;
else
break
end
end
sortedData=sortedData(removeThisMany+1:end);
Fc=Fc(removeThisMany+1:end);
Flow=Flow(removeThisMany+1:end);
Fhigh=Fhigh(removeThisMany+1:end);
%Remove bin at end if unused
if sortedData(end)==0
sortedData=sortedData(1:end-1);
Fc=Fc(1:end-1);
Flow=Flow(1:end-1);
Fhigh=Fhigh(1:end-1);
end
end
