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1 function wts = fft2chromamx(nfft,nbins,sr,A440,ctroct,octwidth)
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2 % wts = fft2chromamx(nfft,nbins,sr,A440,ctroct,octwidth)
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3 % Create a wts matrix to convert FFT to Chroma
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4 % A440 is optional ref frq for A
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5 % ctroct, octwidth specify a dominance window - Gaussian
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6 % weighting centered on ctroct (in octs, re A0 = 27.5Hz) and
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7 % with a gaussian half-width of octwidth. Defaults to
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8 % halfwidth = inf i.e. flat.
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9 % 2006-06-29 dpwe@ee.columbia.edu
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10
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11 if nargin < 2; nbins = 12; end
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12 if nargin < 3; sr = 22050; end
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13 if nargin < 4; A440 = 440; end
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14 if nargin < 5; ctroct = 5; end
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15 if nargin < 6; octwidth = 0; end
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16
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17 wts = zeros(nbins, nfft);
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18
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19 fftfrqbins = nbins*hz2octs([1:(nfft-1)]/nfft*sr,A440);
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20
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21 % make up a value for the 0 Hz bin = 1.5 octaves below bin 1
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22 % (so chroma is 50% rotated from bin 1, and bin width is broad)
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23 fftfrqbins = [fftfrqbins(1)-1.5*nbins,fftfrqbins];
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24
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25 binwidthbins = [max(1, fftfrqbins(2:nfft) - fftfrqbins(1:(nfft-1))), 1];
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26
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27 D = repmat(fftfrqbins,nbins,1) - repmat([0:(nbins-1)]',1,nfft);
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28
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29 nbins2 = round(nbins/2);
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30
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31 % Project into range -nbins/2 .. nbins/2
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32 % add on fixed offset of 10*nbins to ensure all values passed to rem are +ve
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33 D = rem(D + nbins2 + 10*nbins, nbins) - nbins2;
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34
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35 % Gaussian bumps - 2*D to make them narrower
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36 wts = exp(-0.5*(2*D./repmat(binwidthbins,nbins,1)).^2);
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37
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38 % normalize each column
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39 wts = wts./repmat(sqrt(sum(wts.^2)),nbins,1);
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40
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41 % remove aliasing columns
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42 wts(:,[(nfft/2+2):nfft]) = 0;
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43
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44 % Maybe apply scaling for fft bins
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45 if octwidth > 0
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46 wts = wts.*repmat(exp(-0.5*(((fftfrqbins/nbins - ctroct)/octwidth).^2)), nbins, 1);
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47 end
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48
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49 %wts = binwidthbins;
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50 %wts = fftfrqbins;
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51
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52 function octs = hz2octs(freq, A440)
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53 % octs = hz2octs(freq, A440)
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54 % Convert a frequency in Hz into a real number counting
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55 % the octaves above A0. So hz2octs(440) = 4.0
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56 % Optional A440 specifies the Hz to be treated as middle A (default 440).
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57 % 2006-06-29 dpwe@ee.columbia.edu for fft2chromamx
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58
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59 %if nargin < 2; A440 = 440; end
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60
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61 % A4 = A440 = 440 Hz, so A0 = 440/16 Hz
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62 octs = log(freq./(A440/16))./log(2);
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63
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64
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