Create a gist now

Instantly share code, notes, and snippets.

Plot poles and zeros in Z plane for a transfer function
# -*- coding: utf-8 -*-
"""
Combination of
http://scipy-central.org/item/52/1/zplane-function
and
http://www.dsprelated.com/showcode/244.php
with my own modifications
"""
# 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.pyplot import axvline, axhline
from collections import defaultdict
def zplane(z, p, filename=None):
"""Plot the complex z-plane given zeros and poles.
"""
# get a figure/plot
ax = plt.subplot(2, 2, 1)
# TODO: should just inherit whatever subplot it's called in?
# Add unit circle and zero axes
unit_circle = patches.Circle((0,0), radius=1, fill=False,
color='black', ls='solid', alpha=0.1)
ax.add_patch(unit_circle)
axvline(0, color='0.7')
axhline(0, color='0.7')
# Plot the poles and set marker properties
poles = plt.plot(p.real, p.imag, 'x', markersize=9, alpha=0.5)
# Plot the zeros and set marker properties
zeros = plt.plot(z.real, z.imag, 'o', markersize=9,
color='none', alpha=0.5,
markeredgecolor=poles[0].get_color(), # same color as poles
)
# Scale axes to fit
r = 1.5 * np.amax(np.concatenate((abs(z), abs(p), [1])))
plt.axis('scaled')
plt.axis([-r, r, -r, r])
# ticks = [-1, -.5, .5, 1]
# plt.xticks(ticks)
# plt.yticks(ticks)
"""
If there are multiple poles or zeros at the same point, put a
superscript next to them.
TODO: can this be made to self-update when zoomed?
"""
# Finding duplicates by same pixel coordinates (hacky for now):
poles_xy = ax.transData.transform(np.vstack(poles[0].get_data()).T)
zeros_xy = ax.transData.transform(np.vstack(zeros[0].get_data()).T)
# dict keys should be ints for matching, but coords should be floats for
# keeping location of text accurate while zooming
# TODO make less hacky, reduce duplication of code
d = defaultdict(int)
coords = defaultdict(tuple)
for xy in poles_xy:
key = tuple(np.rint(xy).astype('int'))
d[key] += 1
coords[key] = xy
for key, value in d.iteritems():
if value > 1:
x, y = ax.transData.inverted().transform(coords[key])
plt.text(x, y,
r' ${}^{' + str(value) + '}$',
fontsize=13,
)
d = defaultdict(int)
coords = defaultdict(tuple)
for xy in zeros_xy:
key = tuple(np.rint(xy).astype('int'))
d[key] += 1
coords[key] = xy
for key, value in d.iteritems():
if value > 1:
x, y = ax.transData.inverted().transform(coords[key])
plt.text(x, y,
r' ${}^{' + str(value) + '}$',
fontsize=13,
)
if filename is None:
plt.show()
else:
plt.savefig(filename)
print 'Pole-zero plot saved to ' + str(filename)
if __name__ == "__main__":
from scipy.signal import (freqz, butter, bessel, cheby1, cheby2, ellip,
tf2zpk, zpk2tf, lfilter, buttap, bilinear, cheb2ord, cheb2ap
)
from numpy import asarray, tan, array, pi, arange, cos, log10, unwrap, angle
from matplotlib.pyplot import (stem, title, grid, show, plot, xlabel,
ylabel, subplot, xscale, figure, xlim,
margins)
# # Cosine function
# omega = pi/4
# b = array([1.0, -cos(omega)])
# a = array([1, -2*cos(omega), 1.0])
b, a = butter(2, [0.06, 0.7], 'bandpass')
# Get the poles and zeros
z, p, k = tf2zpk(b, a)
# Create zero-pole plot
figure(figsize=(16, 9))
subplot(2, 2, 1)
zplane(z, p)
grid(True, color='0.9', linestyle='-', which='both', axis='both')
title('Poles and zeros')
# Display zeros, poles and gain
print str(len(z)) + " zeros: " + str(z)
print str(len(p)) + " poles: " + str(p)
print "gain: " + str(k)
# Impulse response
index = arange(0,20)
u = 1.0*(index==0)
y = lfilter(b, a, u)
subplot(2, 2, 3)
stem(index,y)
title('Impulse response')
margins(0, 0.1)
grid(True, color='0.9', linestyle='-', which='both', axis='both')
show()
# Frequency response
w, h = freqz(b, a)
subplot(2, 2, 2)
plot(w/pi, 20*log10(abs(h)))
xscale('log')
title('Frequency response')
xlabel('Normalized frequency')
ylabel('Amplitude [dB]')
margins(0, 0.1)
grid(True, color = '0.7', linestyle='-', which='major', axis='both')
grid(True, color = '0.9', linestyle='-', which='minor', axis='both')
show()
# Phase
subplot(2, 2, 4)
plot(w/pi, 180/pi * unwrap(angle(h)))
xscale('log')
xlabel('Normalized frequency')
ylabel('Phase [degrees]')
grid(True, color = '0.7', linestyle='-', which='major')
grid(True, color = '0.9', linestyle='-', which='minor')
show()
@endolith
Owner

bug: alpha only applies to X not O

@heetbeet

Thanks for this gist. I was looking for an easy Matlab replacement and this will do just fine.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment