--- /dev/null
+## Copyright (c) 2007 R.G.H. Eschauzier <reschauzier@yahoo.com>
+## Copyright (c) 2011 Carnë Draug <carandraug+dev@gmail.com>
+## Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+##
+## This program is free software; you can redistribute it and/or modify it under
+## the terms of the GNU General Public License as published by the Free Software
+## Foundation; either version 3 of the License, or (at your option) any later
+## version.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {[@var{b_out}, @var{a_out}] =} impinvar (@var{b}, @var{a}, @var{fs}, @var{tol})
+## @deftypefnx{Function File} {[@var{b_out}, @var{a_out}] =} impinvar (@var{b}, @var{a}, @var{fs})
+## @deftypefnx{Function File} {[@var{b_out}, @var{a_out}] =} impinvar (@var{b}, @var{a})
+## Converts analog filter with coefficients @var{b} and @var{a} to digital,
+## conserving impulse response.
+##
+## If @var{fs} is not specificied, or is an empty vector, it defaults to 1Hz.
+##
+## If @var{tol} is not specified, it defaults to 0.0001 (0.1%)
+## This function does the inverse of impinvar so that the following example should
+## restore the original values of @var{a} and @var{b}.
+##
+## @command{invimpinvar} implements the reverse of this function.
+## @example
+## [b, a] = impinvar (b, a);
+## [b, a] = invimpinvar (b, a);
+## @end example
+##
+## Reference: Thomas J. Cavicchi (1996) ``Impulse invariance and multiple-order
+## poles''. IEEE transactions on signal processing, Vol 40 (9): 2344--2347
+##
+## @seealso{bilinear, invimpinvar}
+## @end deftypefn
+
+function [b_out, a_out] = impinvar (b_in, a_in, fs = 1, tol = 0.0001)
+
+ if (nargin <2)
+ print_usage;
+ endif
+
+ ## to be compatible with the matlab implementation where an empty vector can
+ ## be used to get the default
+ if (isempty(fs))
+ ts = 1;
+ else
+ ts = 1/fs; # we should be using sampling frequencies to be compatible with Matlab
+ endif
+
+ [r_in, p_in, k_in] = residue(b_in, a_in); % partial fraction expansion
+
+ n = length(r_in); % Number of poles/residues
+
+ if (length(k_in)>0) % Greater than zero means we cannot do impulse invariance
+ error("Order numerator >= order denominator");
+ endif
+
+ r_out = zeros(1,n); % Residues of H(z)
+ p_out = zeros(1,n); % Poles of H(z)
+ k_out = 0; % Contstant term of H(z)
+
+ i=1;
+ while (i<=n)
+ m = 1;
+ first_pole = p_in(i); % Pole in the s-domain
+ while (i<n && abs(first_pole-p_in(i+1))<tol) % Multiple poles at p(i)
+ i++; % Next residue
+ m++; % Next multiplicity
+ endwhile
+ [r, p, k] = z_res(r_in(i-m+1:i), first_pole, ts); % Find z-domain residues
+ k_out += k; % Add direct term to output
+ p_out(i-m+1:i) = p; % Copy z-domain pole(s) to output
+ r_out(i-m+1:i) = r; % Copy z-domain residue(s) to output
+
+ i++; % Next s-domain residue/pole
+ endwhile
+
+ [b_out, a_out] = inv_residue(r_out, p_out, k_out, tol);
+ a_out = to_real(a_out); % Get rid of spurious imaginary part
+ b_out = to_real(b_out);
+
+ % Shift results right to account for calculating in z instead of z^-1
+ b_out(end)=[];
+
+endfunction
+
+## Convert residue vector for single and multiple poles in s-domain (located at sm) to
+## residue vector in z-domain. The variable k is the direct term of the result.
+function [r_out, p_out, k_out] = z_res (r_in, sm, ts)
+
+ p_out = exp(ts * sm); % z-domain pole
+ n = length(r_in); % Multiplicity of the pole
+ r_out = zeros(1,n); % Residue vector
+
+ %% First pole (no multiplicity)
+ k_out = r_in(1) * ts; % PFE of z/(z-p) = p/(z-p)+1; direct part
+ r_out(1) = r_in(1) * ts * p_out; % pole part of PFE
+
+ for i=(2:n) % Go through s-domain residues for multiple pole
+ r_out(1:i) += r_in(i) * polyrev(h1_z_deriv(i-1, p_out, ts)); % Add z-domain residues
+ endfor
+
+endfunction
+
+
+%!function err = stozerr(bs,as,fs)
+%!
+%! % number of time steps
+%! n=100;
+%!
+%! % impulse invariant transform to z-domain
+%! [bz az]=impinvar(bs,as,fs);
+%!
+%! % create sys object of transfer function
+%! s=tf(bs,as);
+%!
+%! % calculate impulse response of continuous time system
+%! % at discrete time intervals 1/fs
+%! ys=impulse(s,(n-1)/fs,1/fs)';
+%!
+%! % impulse response of discrete time system
+%! yz=filter(bz,az,[1 zeros(1,n-1)]);
+%!
+%! % find rms error
+%! err=sqrt(sum((yz*fs.-ys).^2)/length(ys));
+%! endfunction
+%!
+%!assert(stozerr([1],[1 1],100),0,0.0001);
+%!assert(stozerr([1],[1 2 1],100),0,0.0001);
+%!assert(stozerr([1 1],[1 2 1],100),0,0.0001);
+%!assert(stozerr([1],[1 3 3 1],100),0,0.0001);
+%!assert(stozerr([1 1],[1 3 3 1],100),0,0.0001);
+%!assert(stozerr([1 1 1],[1 3 3 1],100),0,0.0001);
+%!assert(stozerr([1],[1 0 1],100),0,0.0001);
+%!assert(stozerr([1 1],[1 0 1],100),0,0.0001);
+%!assert(stozerr([1],[1 0 2 0 1],100),0,0.0001);
+%!assert(stozerr([1 1],[1 0 2 0 1],100),0,0.0001);
+%!assert(stozerr([1 1 1],[1 0 2 0 1],100),0,0.0001);
+%!assert(stozerr([1 1 1 1],[1 0 2 0 1],100),0,0.0001);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff