Re: How to smooth FFT data on logarithmic frequency bins (octave bands)?

[Juan Pablo Carbajal]

On Fri, Jul 3, 2015 at 11:20 PM, Matthias Brennwald
<address@hidden> wrote:
> Hi all
>
> I calculated the frequency response of a loudspeaker from the impulse 
> response. Now I'd like to smooth the response, e.g. in a 1/24 octave band 
> (octave, not Octave). I do this by defining the frequency bins (e.g., 1/24 
> octave bins) and then loop through these bins, find the data in the frequency 
> range of each bin, and calculate the means of each bin (see code example 
> below). This (i) slow and (ii) not elegant.
>
> Does someone have an idea on how to improve this? Is there a way to transform 
> the data such that the loop can be avoided?
>
> In addition, it would be nice to use a more elaborate method than just 
> calculating the means of each bin. For instance, something similar to a 
> Savitzky-Golay smoothing would be nice.
>
> Thanks for your help!
>
> Matthias
>
> =============================
> Code example of my current approach:
> =============================
>
> % raw frequency response (before smoothing):
> f = 10:10:40000;                        % frequency values of loudspeaker 
> frequency response
> Y = 10 + rand(size(f));         % frequency response (absolute values of 
> Fourier transporm)
>
> % 1/24 octave smoothing:
> sm = 1/24;                                                              % 
> smoothing band width (fraction of an octave)
> n  = floor ( log2(f(end)/f(1)) / sm );  % number of frequency bins for 
> avaraging
> YY = repmat (NaN,1,n); ff = repmat (NaN,size(YY)); % initialize vectors that 
> will contain the smoothed data
> f1 = f(1);      % lower end of first frequency bin
> for i = 1:n     % loop through frequency bins and calculate means of each bin
>         f2 = f1*2^sm;   % upper end of frequency bin
>         ff(i) = sqrt(f1*f2); % center frequency of current bin
>         j = find (f >= f1 & f < f2); % find data in frequency bin f1...f2
>         if any (j) % compute mean
>                 YY(i) = mean (Y(j));
>         end
>         f1 = f2; % prepare for next iteration
> end
>
> % remove missing / NaN entries:
> i = find (~isnan(YY));
> ff = ff(i); YY = YY(i);
>
> plot (f,Y,'k-','linewidth',1 , ff,YY,'r-','linewidth',5);
> legend ('Raw','Smoothed 1/24 octave’)
>
> =============================
>
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The signal package has sgolayfilt, there is also the smooth function.