V_LPCSS2ZZ Convert s-plane poles to z-plane poles ZZ=(SS,NR)
Inputs: ss(n,q) n frames each with q complex-valued pole positions in normalized-Hz units.
A formant with frequency f (in range 0 to 0.5) and bandwidth b will give an
s-plane pole-pair of approximately (-b/2 +-j*f)/fs where fs is the sample frequency.
nr Optional argument specifying how many of the q poles should *not* be
supplemented by including their conjugate pair. The conjugates of poles nr+1:q
will be appended to ss as additional columns. As a special case, nr=-1
will include the conjugate of any column containing a non-real number.
Outputs: zz(n,p) z-plane poles. If nr is omitted, then p=q; if nr>=0, then p=2*q-nr.
The inverse function is zz=v_lpczz2ss(zz)0001 function zz=v_lpcss2zz(ss,nr) 0002 %V_LPCSS2ZZ Convert s-plane poles to z-plane poles ZZ=(SS,NR) 0003 % 0004 % Inputs: ss(n,q) n frames each with q complex-valued pole positions in normalized-Hz units. 0005 % A formant with frequency f (in range 0 to 0.5) and bandwidth b will give an 0006 % s-plane pole-pair of approximately (-b/2 +-j*f)/fs where fs is the sample frequency. 0007 % nr Optional argument specifying how many of the q poles should *not* be 0008 % supplemented by including their conjugate pair. The conjugates of poles nr+1:q 0009 % will be appended to ss as additional columns. As a special case, nr=-1 0010 % will include the conjugate of any column containing a non-real number. 0011 % 0012 % Outputs: zz(n,p) z-plane poles. If nr is omitted, then p=q; if nr>=0, then p=2*q-nr. 0013 % 0014 % The inverse function is zz=v_lpczz2ss(zz) 0015 0016 % Copyright (C) Mike Brookes 1997-2025 0017 % 0018 % VOICEBOX is a MATLAB toolbox for speech processing. 0019 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0020 % 0021 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0022 % This program is free software; you can redistribute it and/or modify 0023 % it under the terms of the GNU Lesser General Public License as published by 0024 % the Free Software Foundation; either version 3 of the License, or 0025 % (at your option) any later version. 0026 % 0027 % This program is distributed in the hope that it will be useful, 0028 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0029 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0030 % GNU Lesser General Public License for more details. 0031 % 0032 % You can obtain a copy of the GNU Lesser General Public License from 0033 % https://www.gnu.org/licenses/ . 0034 % See files gpl-3.0.txt and lgpl-3.0.txt included in this distribution. 0035 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0036 if nargin>1 && nr<size(ss,2) 0037 if nr>=0 0038 ss=[ss conj(ss(:,nr+1:end))]; 0039 else 0040 ss=[ss conj(ss(:,any(imag(ss)~=0,1)))]; 0041 end 0042 end 0043 zz=exp(2*pi*ss); 0044 if ~nargout 0045 q=(0:200)*2*pi/200; 0046 plot(real(zz.'),imag(zz.'),'x',cos(q),sin(q),':k',[-1.05 0; 1.05 0],[0 -1.05; 0 1.05],':k'); 0047 axis([-1.05 1.05 -1.05 1.05]); 0048 axis equal; 0049 xlabel('Real'); 0050 ylabel('Imag'); 0051 end 0052