FRQ2ERB Convert Hertz to ERB frequency scale ERB=(FRQ) erb = frq2erb(frq) converts a vector of frequencies (in Hz) to the corresponding values on the ERB-rate scale on which the human ear has roughly constant resolution as judged by psychophysical measurements of the cochlear filters. The inverse function is erb2frq.

- xticksi XTIXKSI labels the x-axis of a plot using SI multipliers S=(AH)
- yticksi YTIXKSI labels the y-axis of a plot using SI multipliers S=(AH)

- filtbankm FILTBANKM determine matrix for a linear/mel/erb/bark-spaced filterbank [X,MN,MX]=(P,N,FS,FL,FH,W)
- gammabank GAMMABANK gammatone filter bank [b,a,fx,bx,gd]=(n,fs,w,fc,bw,ph,k)
- melbankm MELBANKM determine matrix for a mel/erb/bark-spaced filterbank [X,MN,MX]=(P,N,FS,FL,FH,W)
- spgrambw SPGRAMBW Draw spectrogram [T,F,B]=(s,fs,mode,bw,fmax,db,tinc,ann)

0001 function [erb,bnd] = frq2erb(frq) 0002 %FRQ2ERB Convert Hertz to ERB frequency scale ERB=(FRQ) 0003 % erb = frq2erb(frq) converts a vector of frequencies (in Hz) 0004 % to the corresponding values on the ERB-rate scale on which 0005 % the human ear has roughly constant resolution as judged by 0006 % psychophysical measurements of the cochlear filters. The 0007 % inverse function is erb2frq. 0008 0009 % The erb scale is measured using the notched-noise method [3]. 0010 % 0011 % We have df/de = 6.23*f^2 + 93.39*f + 28.52 0012 % where the above expression gives the Equivalent Rectangular 0013 % Bandwidth (ERB)in Hz of a human auditory filter with a centre 0014 % frequency of f kHz. 0015 % 0016 % By integrating the reciprocal of the above expression, we 0017 % get: 0018 % e = a ln((f/p-1)/(f/q-1)) 0019 % 0020 % where p and q are the roots of the equation: -0.312 and -14.7 0021 % and a = 1000/(6.23*(p-q)) = 11.17268 0022 % 0023 % We actually implement e as 0024 % 0025 % e = a ln (1 + b*f/(f+c)) 0026 % 0027 % where b = q/p - 1 = 46.06538 0028 % c = -1000q = 14678.49 0029 % and f is in Hz 0030 % 0031 % References: 0032 % 0033 % [1] B.C.J.Moore & B.R.Glasberg "Suggested formula for 0034 % calculating auditory-filter bandwidth and excitation 0035 % patterns", J Acoust Soc America V74, pp 750-753, 1983 0036 % [2] O. Ghitza, "Auditory Models & Human Performance in Tasks 0037 % related to Speech Coding & Speech Recognition", 0038 % IEEE Trans on Speech & Audio Processing, Vol 2, 0039 % pp 115-132, Jan 1994 0040 % [3] R. D. Patterson. Auditory filter shapes derived with noise 0041 % stimuli. J. Acoust. Soc. Amer., 59: 640–654, 1976. 0042 0043 % Copyright (C) Mike Brookes 1998 0044 % Version: $Id: frq2erb.m 4501 2014-04-24 06:28:21Z dmb $ 0045 % 0046 % VOICEBOX is a MATLAB toolbox for speech processing. 0047 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0048 % 0049 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0050 % This program is free software; you can redistribute it and/or modify 0051 % it under the terms of the GNU General Public License as published by 0052 % the Free Software Foundation; either version 2 of the License, or 0053 % (at your option) any later version. 0054 % 0055 % This program is distributed in the hope that it will be useful, 0056 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0057 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0058 % GNU General Public License for more details. 0059 % 0060 % You can obtain a copy of the GNU General Public License from 0061 % http://www.gnu.org/copyleft/gpl.html or by writing to 0062 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0063 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0064 g=abs(frq); 0065 erb=11.17268*sign(frq).*log(1+46.06538*g./(g+14678.49)); 0066 bnd=6.23e-6*g.^2 + 93.39e-3*g + 28.52; 0067 if ~nargout 0068 plot(frq,erb,'-x'); 0069 xlabel(['Frequency (' xticksi 'Hz)']); 0070 ylabel(['Frequency (' yticksi 'Erb-rate)']); 0071 end

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