hello
this is a code that does what you are looking for
now this simply do a linear average of the spectrum amplitude between each lower / upper frequency bound
if your spectrum is given in dB , you have to convert first back to linear scale and do the conversion,then do the dB conversion (with averaging) of the 1/3 octave spectrum
% conversion fft narrow band spectrum to 1/3 octave
%% dummy data
freq = linspace(100,1000,100);
spectrum = 25+5*randn(size(freq));
[fto,sTO] = conversion2TO(freq,spectrum);
figure(1), plot(freq,spectrum,'b',fto,sTO,'*-r');
legend('narrow band FFT spectrum','1/3 octave band spectrum');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [fto,sTO] = conversion2TO(freq,spectrum)
% normalized 1/3 octave center freqs
fref = [10, 12.5 16 20, 25 31.5 40, 50 63 80, 100 125 160, 200 250 315, ...
400 500 630, 800 1000 1250, 1600 2000 2500, 3150 4000 5000, ...
6300 8000 10000, 12500 16000 20000 ];
ff = (1000).*((2^(1/3)).^[-20:13]); % Exact center freq.
a = sqrt(2^(1/3)); %
f_lower_bound = ff./a;
f_higher_bound = ff.*a;
ind1 = find (f_higher_bound>min(freq)); ind1 = ind1(1); % indice of first value of "f_higher_bound" above "min(freq)"
ind2 = find (f_lower_bound<max(freq)); ind2 = ind2(end); % indice of last value "f_lower_bound" below "max(freq)"
ind3 = (ind1:ind2);
for ci = 1:length(ind3)
ind4 = find(freq>=f_lower_bound(ind3(ci)) & freq<=f_higher_bound(ind3(ci)));
sTO(ci) = mean(spectrum(ind4)); % 1/3 octave value = averaged value of spectrum inside 1/3 octave band
fto(ci) = fref(ind3(ci)); % valid central frequency 1/3 octave
end
end
