Hi all, I'am not sure if this is the right place - but I try it ;)
I tried to contact pkien...@kienzle.powernet.co.uk, the original author of zplane.m, but the address seems to be dead. Maybe someone here can help. There is a problem with zplane.m. the markers for poles and zeroes are far to small - if they are on the unit circle one can't see them at all. (I use the Version from the Ubuntu repos) It is simple to fix this problem by changing the setting in the .m-file. (attached). But I'am unsure if there was a reason to make the markers this small? If not is someone able to get this into the main distribution of the signal package? Thanks! Simon
## Copyright (C) 1999 Paul Kienzle ## ## 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 2 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 []. ## 2001-03-17 Paul Kienzle ## * extend axes to include all points outside the unit circle ## 2004-04-20 Stefan van der Walt ## * plot correct nr of zeros at 0 ## * label nr of zeros/poles at a point ## * use different colours for plotting each column (matrix zeros/poles) ## * set automatic_replot to 0 for duration of demo ## 2009-11-15 Simon Schwarz ## * changed the standard size of the markers to 12 ## 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) usage("zplane(b [, a]) or zplane(z [, p])"); end if nargin < 2, p=[]; endif 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"); replot; 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', 12); endif if (!isempty(z)) h = plot(real(z), imag(z), "bo"); set (h, 'MarkerSize', 12); 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]);
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