V_FRQ2ERB Convert Hertz to ERB frequency scale ERB=(FRQ)
erb = v_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 v_erb2frq.0001 function [erb,bnd] = v_frq2erb(frq) 0002 %V_FRQ2ERB Convert Hertz to ERB frequency scale ERB=(FRQ) 0003 % erb = v_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 v_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 (h - k/(f+c)) 0026 % 0027 % where k = 1000(q - q^2/p) = 676170.42 0028 % h = q/p = 47.065 0029 % c = -1000q = 14678.49 0030 % and f is in Hz 0031 % 0032 % References: 0033 % 0034 % [1] B.C.J.Moore & B.R.Glasberg "Suggested formula for 0035 % calculating auditory-filter bandwidth and excitation 0036 % patterns", J Acoust Soc America V74, pp 750-753, 1983 0037 % [2] O. Ghitza, "Auditory Models & Human Performance in Tasks 0038 % related to Speech Coding & Speech Recognition", 0039 % IEEE Trans on Speech & Audio Processing, Vol 2, 0040 % pp 115-132, Jan 1994 0041 % [3] R. D. Patterson. Auditory filter shapes derived with noise 0042 % stimuli. J. Acoust. Soc. Amer., 59:640-654, 1976. 0043 % [4] B. Glasberg and B. Moore. Derivation of auditory filter shapes from 0044 % notched-noise data. Hearing Research, 47(1-2):103–138, 1990. 0045 % doi: 10.1016/0378-5955(90)90170-T. 0046 0047 % Copyright (C) Mike Brookes 1998-2015 0048 % Version: $Id: v_frq2erb.m 10865 2018-09-21 17:22:45Z dmb $ 0049 % 0050 % VOICEBOX is a MATLAB toolbox for speech processing. 0051 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0052 % 0053 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0054 % This program is free software; you can redistribute it and/or modify 0055 % it under the terms of the GNU General Public License as published by 0056 % the Free Software Foundation; either version 2 of the License, or 0057 % (at your option) any later version. 0058 % 0059 % This program is distributed in the hope that it will be useful, 0060 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0061 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0062 % GNU General Public License for more details. 0063 % 0064 % You can obtain a copy of the GNU General Public License from 0065 % http://www.gnu.org/copyleft/gpl.html or by writing to 0066 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0067 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0068 persistent u a h k c 0069 if ~numel(u) 0070 u=[6.23e-6 93.39e-3 28.52]; % from equation (3) in [1] (an simpler formula is (3) in [4]) 0071 p=sort(roots(u)); % p=[-14678.5 -311.9] 0072 a=1e6/(6.23*(p(2)-p(1))); % a=11.17 0073 c=p(1); % c=-14678.5 0074 k = p(1) - p(1)^2/p(2); % k=676170.42 0075 h=p(1)/p(2); % h=47.065 0076 end 0077 g=abs(frq); 0078 % erb=11.17268*sign(frq).*log(1+46.06538*g./(g+14678.49)); 0079 erb=a*sign(frq).*log(h-k./(g-c)); 0080 bnd=polyval(u,g); 0081 if ~nargout 0082 plot(frq,erb,'-x'); 0083 xlabel(['Frequency (' v_xticksi 'Hz)']); 0084 ylabel(['Frequency (' v_yticksi 'Erb-rate)']); 0085 end