--- /dev/null
+## Copyright (C) 1999, 2001 Paul Kienzle <pkienzle@users.sf.net>
+## Copyright (C) 2004 Stefan van der Walt <stefan@sun.ac.za>
+##
+## 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/>.
+
+## usage: zplane(b [, a]) or zplane(z [, p])
+##
+## Plot the poles and zeros. If the arguments are row vectors then they
+## represent filter coefficients (numerator polynomial b and denominator
+## polynomial a), but if they are column vectors or matrices then they
+## represent poles and zeros.
+##
+## This is a horrid interface, but I didn't choose it; better would be
+## to accept b,a or z,p,g like other functions. The saving grace is
+## that poly(x) always returns a row vector and roots(x) always returns
+## a column vector, so it is usually right. You must only be careful
+## when you are creating filters by hand.
+##
+## Note that due to the nature of the roots() function, poles and zeros
+## may be displayed as occurring around a circle rather than at a single
+## point.
+##
+## The transfer function is
+##
+## B(z) b0 + b1 z^(-1) + b2 z^(-2) + ... + bM z^(-M)
+## H(z) = ---- = --------------------------------------------
+## A(z) a0 + a1 z^(-1) + a2 z^(-2) + ... + aN z^(-N)
+##
+## b0 (z - z1) (z - z2) ... (z - zM)
+## = -- z^(-M+N) ------------------------------
+## a0 (z - p1) (z - p2) ... (z - pN)
+##
+## The denominator a defaults to 1, and the poles p defaults to [].
+
+## TODO: Consider a plot-like interface:
+## TODO: zplane(x1,y1,fmt1,x2,y2,fmt2,...)
+## TODO: with y_i or fmt_i optional as usual. This would allow
+## TODO: legends and control over point colour and filters of
+## TODO: different orders.
+function zplane(z, p = [])
+
+ if (nargin < 1 || nargin > 2)
+ print_usage;
+ end
+ if columns(z)>1 || columns(p)>1
+ if rows(z)>1 || rows(p)>1
+ ## matrix form: columns are already zeros/poles
+ else
+ ## z -> b
+ ## p -> a
+ if isempty(z), z=1; endif
+ if isempty(p), p=1; endif
+
+ M = length(z) - 1;
+ N = length(p) - 1;
+ z = [ roots(z); zeros(N - M, 1) ];
+ p = [ roots(p); zeros(M - N, 1) ];
+ endif
+ endif
+
+
+ xmin = min([-1; real(z(:)); real(p(:))]);
+ xmax = max([ 1; real(z(:)); real(p(:))]);
+ ymin = min([-1; imag(z(:)); imag(p(:))]);
+ ymax = max([ 1; imag(z(:)); imag(p(:))]);
+ xfluff = max([0.05*(xmax-xmin), (1.05*(ymax-ymin)-(xmax-xmin))/10]);
+ yfluff = max([0.05*(ymax-ymin), (1.05*(xmax-xmin)-(ymax-ymin))/10]);
+ xmin = xmin - xfluff;
+ xmax = xmax + xfluff;
+ ymin = ymin - yfluff;
+ ymax = ymax + yfluff;
+
+ text();
+ plot_with_labels(z, "o");
+ plot_with_labels(p, "x");
+ refresh;
+
+ r = exp(2i*pi*[0:100]/100);
+ plot(real(r), imag(r),'k'); hold on;
+ axis equal;
+ grid on;
+ axis(1.05*[xmin, xmax, ymin, ymax]);
+ if (!isempty(p))
+ h = plot(real(p), imag(p), "bx");
+ set (h, 'MarkerSize', 7);
+ endif
+ if (!isempty(z))
+ h = plot(real(z), imag(z), "bo");
+ set (h, 'MarkerSize', 7);
+ endif
+ hold off;
+endfunction
+
+function plot_with_labels(x, symbol)
+ if ( !isempty(x) )
+
+ x_u = unique(x(:));
+
+ for i = 1:length(x_u)
+ n = sum(x_u(i) == x(:));
+ if (n > 1)
+ text(real(x_u(i)), imag(x_u(i)), [" " num2str(n)]);
+ endif
+ endfor
+
+ col = "rgbcmy";
+ for c = 1:columns(x)
+ plot(real( x(:,c) ), imag( x(:,c) ), [col(mod(c,6)),symbol ";;"]);
+ endfor
+
+ endif
+endfunction
+
+%!demo
+%! ## construct target system:
+%! ## symmetric zero-pole pairs at r*exp(iw),r*exp(-iw)
+%! ## zero-pole singletons at s
+%! pw=[0.2, 0.4, 0.45, 0.95]; #pw = [0.4];
+%! pr=[0.98, 0.98, 0.98, 0.96]; #pr = [0.85];
+%! ps=[];
+%! zw=[0.3]; # zw=[];
+%! zr=[0.95]; # zr=[];
+%! zs=[];
+%!
+%! ## system function for target system
+%! p=[[pr, pr].*exp(1i*pi*[pw, -pw]), ps]';
+%! z=[[zr, zr].*exp(1i*pi*[zw, -zw]), zs]';
+%! M = length(z); N = length(p);
+%! sys_a = [ zeros(1, M-N), real(poly(p)) ];
+%! sys_b = [ zeros(1, N-M), real(poly(z)) ];
+%! disp("The first two graphs should be identical, with poles at (r,w)=");
+%! disp(sprintf(" (%.2f,%.2f)", [pr ; pw]));
+%! disp("and zeros at (r,w)=");
+%! disp(sprintf(" (%.2f,%.2f)", [zr ; zw]));
+%! disp("with reflection across the horizontal plane");
+%! subplot(231); title("transfer function form"); zplane(sys_b, sys_a);
+%! subplot(232); title("pole-zero form"); zplane(z,p);
+%! subplot(233); title("empty p"); zplane(z);
+%! subplot(234); title("empty a"); zplane(sys_b);
+%! disp("The matrix plot has 2 sets of points, one inside the other");
+%! subplot(235); title("matrix"); zplane([z, 0.7*z], [p, 0.7*p]);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff