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| # | |
| # Copyright (c) 2011 Christopher Felton | |
| # | |
| # This program is free software: you can redistribute it and/or modify | |
| # it under the terms of the GNU Lesser 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 Lesser General Public License for more details. | |
| # | |
| # You should have received a copy of the GNU Lesser General Public License | |
| # along with this program. If not, see <http://www.gnu.org/licenses/>. | |
| # | |
| # The following is derived from the slides presented by | |
| # Alexander Kain for CS506/606 "Special Topics: Speech Signal Processing" | |
| # CSLU / OHSU, Spring Term 2011. | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| from matplotlib import patches | |
| from matplotlib.figure import Figure | |
| from matplotlib import rcParams | |
| def zplane(b,a,filename=None): | |
| """Plot the complex z-plane given a transfer function. | |
| """ | |
| # get a figure/plot | |
| ax = plt.subplot(111) | |
| # create the unit circle | |
| uc = patches.Circle((0,0), radius=1, fill=False, | |
| color='black', ls='dashed') | |
| ax.add_patch(uc) | |
| # The coefficients are less than 1, normalize the coeficients | |
| if np.max(b) > 1: | |
| kn = np.max(b) | |
| b = b/float(kn) | |
| else: | |
| kn = 1 | |
| if np.max(a) > 1: | |
| kd = np.max(a) | |
| a = a/float(kd) | |
| else: | |
| kd = 1 | |
| # Get the poles and zeros | |
| p = np.roots(a) | |
| z = np.roots(b) | |
| k = kn/float(kd) | |
| # Plot the zeros and set marker properties | |
| t1 = plt.plot(z.real, z.imag, 'go', ms=10) | |
| plt.setp( t1, markersize=10.0, markeredgewidth=1.0, | |
| markeredgecolor='k', markerfacecolor='g') | |
| # Plot the poles and set marker properties | |
| t2 = plt.plot(p.real, p.imag, 'rx', ms=10) | |
| plt.setp( t2, markersize=12.0, markeredgewidth=3.0, | |
| markeredgecolor='r', markerfacecolor='r') | |
| ax.spines['left'].set_position('center') | |
| ax.spines['bottom'].set_position('center') | |
| ax.spines['right'].set_visible(False) | |
| ax.spines['top'].set_visible(False) | |
| # set the ticks | |
| r = 1.5; plt.axis('scaled'); plt.axis([-r, r, -r, r]) | |
| ticks = [-1, -.5, .5, 1]; plt.xticks(ticks); plt.yticks(ticks) | |
| if filename is None: | |
| plt.show() | |
| else: | |
| plt.savefig(filename) | |
| return z, p, k |
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