V_ERB2FRQ Convert ERB frequency scale to Hertz FRQ=(ERB)
frq = v_erb2frq(erb) converts a vector of ERB-rate values
to the corresponding frequencies in Hz.
[frq,bnd] = v_erb2frq(erb) also calculates the ERB bandwidths
Note that erb values will be clipped to 43.032 which corresponds to infinite frequency.
The inverse function is v_frq2erb.0001 function [frq,bnd] = v_erb2frq(erb) 0002 %V_ERB2FRQ Convert ERB frequency scale to Hertz FRQ=(ERB) 0003 % frq = v_erb2frq(erb) converts a vector of ERB-rate values 0004 % to the corresponding frequencies in Hz. 0005 % [frq,bnd] = v_erb2frq(erb) also calculates the ERB bandwidths 0006 % 0007 % Note that erb values will be clipped to 43.032 which corresponds to infinite frequency. 0008 % The inverse function is v_frq2erb. 0009 0010 % The erb scale is measured using the notched-noise method [3]. 0011 % 0012 % We have df/de = 6.23*f^2 + 93.39*f + 28.52 0013 % where the above expression gives the Equivalent Rectangular 0014 % Bandwidth (ERB)in Hz of a human auditory filter with a centre 0015 % frequency of f kHz. 0016 % 0017 % By integrating the reciprocal of the above expression, we 0018 % get: 0019 % e = k ln((f/p-1)/(f/q-1))/d 0020 % 0021 % where p and q are the roots of the equation: -0.312 and -14.7 0022 % and d = (6.23*(p-q))/1000 = 0.08950404 0023 % 0024 % from this we can derive: 0025 % 0026 % f = k/(h-exp(d*e)) + c 0027 % 0028 % where k = 1000 q (1 - q/p) = 676170.4 0029 % h = q/p = 47.06538 0030 % c = 1000q = -14678.49 0031 % and f is in Hz 0032 % 0033 % Note that the maximum permissible value of e is log(b)/c=43.032 since this gives f=inf 0034 % 0035 % References: 0036 % 0037 % [1] B.C.J.Moore & B.R.Glasberg "Suggested formula for 0038 % calculating auditory-filter bandwidth and excitation 0039 % patterns", J Acoust Soc America V74, pp 750-753, 1983 0040 % [2] O. Ghitza, "Auditory Models & Human Performance in Tasks 0041 % related to Speech Coding & Speech Recognition", 0042 % IEEE Trans on Speech & Audio Processing, Vol 2, 0043 % pp 115-132, Jan 1994 0044 % [3] R. D. Patterson. Auditory filter shapes derived with noise 0045 % stimuli. J. Acoust. Soc. Amer., 59: 640�654, 1976. 0046 % 0047 0048 % Copyright (C) Mike Brookes 1998 0049 % Version: $Id: v_erb2frq.m 10865 2018-09-21 17:22:45Z dmb $ 0050 % 0051 % VOICEBOX is a MATLAB toolbox for speech processing. 0052 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0053 % 0054 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0055 % This program is free software; you can redistribute it and/or modify 0056 % it under the terms of the GNU General Public License as published by 0057 % the Free Software Foundation; either version 2 of the License, or 0058 % (at your option) any later version. 0059 % 0060 % This program is distributed in the hope that it will be useful, 0061 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0062 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0063 % GNU General Public License for more details. 0064 % 0065 % You can obtain a copy of the GNU General Public License from 0066 % http://www.gnu.org/copyleft/gpl.html or by writing to 0067 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0068 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0069 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0070 persistent u h k c d 0071 if ~numel(u) 0072 u=[6.23e-6 93.39e-3 28.52]; 0073 p=sort(roots(u)); % p=[-14678.5 -311.9] 0074 d=1e-6*(6.23*(p(2)-p(1))); % d=0.0895 0075 c=p(1); % c=-14678.5 0076 k = p(1) - p(1)^2/p(2); % k=676170.4 0077 h=p(1)/p(2); % h=47.06538 0078 end 0079 frq = sign(erb).*(k./max(h-exp(d*abs(erb)),0)+c); 0080 bnd=polyval(u,abs(frq)); 0081 if ~nargout 0082 plot(erb,frq,'-x'); 0083 xlabel(['Frequency (' v_xticksi 'Erb-rate)']); 0084 ylabel(['Frequency (' v_yticksi 'Hz)']); 0085 end