Minimum_and_maximum_phase_responses.gif
Summary
Description Minimum and maximum phase responses.gif |
English:
Shows the phase responses of a minimum and maximum phase responses when
is a monomial with
. Both filters have the same gain response. Top : Minimum phase filter. Bottom : Maximum phase filter. Left : Nyquist diagram. Right : Phase responses
|
Date | |
Source | Own work |
Author | fdeloche |
Licensing
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license.
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Generation code
Minimumphase.py # coding: utf-8 '''Generate an animation showing the phase response for a minimum and maximum phase system''' __author__ = "fdeloche" # In[1]: get_ipython().magic(u'matplotlib inline') import sys import numpy as np import matplotlib.pyplot as pl from matplotlib.animation import FuncAnimation # In[2]: createGif=True pl.rc('xtick', labelsize=20) pl.rc('ytick', labelsize=20) pl.rc('font', weight='bold') # In[3]: fig, ((ax1, ax2), (ax3, ax4)) = pl.subplots(2, 2, figsize=(15, 15)) #fig.set_tight_layout(True) a_x = 0.8 a_y=0. m=1000 A = a_x + 1j*a_y a_mod = np.abs(A) Ainv = 1./A a_xbis = np.real(Ainv) a_ybis = -np.imag(Ainv) # r^2 = x_lim_a = -0.3 x_lim_b = 1.9 y_lim = 1.1 t = np.linspace(0, 1, num=m) ax1.scatter(0, 0, linewidth=6, color='blue') ax1.scatter(1, 0, linewidth=4, color='blue') ax1.set_xlim([x_lim_a, x_lim_b]) ax1.set_ylim([-y_lim, y_lim]) ax1.set_title('$1-az^{-1}$', fontsize=35) ax1.plot(t, np.zeros(m), color='blue', linewidth=4) ax1.plot(1+a_mod*np.cos(2*np.pi*t), a_mod*np.sin(2*np.pi*t), color='black') ax1.axis('off') ax1.text(-0.2, 0.1, "$(0, 0)$", fontsize=30, color='blue') ax1.text(1-0.1, 0.1, "$(1, 0)$", fontsize=30, color='blue') ax3.set_title('$\overline{a}(1-\overline{a}^{\ -1}z^{-1})$', fontsize=35) ax3.scatter(0, 0, linewidth=6, color='blue') ax3.scatter(np.abs(A), 0, linewidth=4, color='blue') ax3.set_xlim([x_lim_a, x_lim_b]) ax3.set_ylim([-y_lim, y_lim]) ax3.plot(t*np.abs(A), np.zeros(m), color='blue', linewidth=4) ax3.plot(np.abs(A)+np.cos(2*np.pi*t), np.sin(2*np.pi*t), color='black') ax3.axis('off') ax3.text(-0.1, 0.1, "$(0, 0)$", fontsize=30, color='blue') ax3.text(-0.1+np.abs(A), 0.1, "$(\overline{a}, 0)$", fontsize=30, color='blue') Z = np.cos(2*np.pi*t) - 1j*np.sin(2*np.pi*t) G = np.angle(1-A*Z) ax2.set_title('Phase response', fontsize=25) ax2.plot(2*np.pi*t, G, color='blue', linewidth=2) ax2.plot(2*np.pi*t, 0*t, color='black') G2 = np.angle(1-np.conj(Ainv)*Z) #ax4.set_title('Phase response', fontsize=25) ax4.plot(2*np.pi*t, G2, color='blue', linewidth=2) ax4.plot(2*np.pi*t, 0*t, color='black') ax2.set_ylim([-np.pi, np.pi]) ax4.set_ylim([-np.pi, np.pi]) ax2.set_xlim([0, 6.283]) ax4.set_xlim([0, 6.283]) ''' ax2.spines["top"].set_visible(False) ax2.spines["right"].set_visible(False) ax4.spines["top"].set_visible(False) ax4.spines["right"].set_visible(False) ''' # In[4]: line1, = ax1.plot(1-np.abs(A)*t*1, t*0, color='blue', linewidth=4) line2, = ax3.plot(np.abs(A)-t*1, t*0, color='blue', linewidth=4) line3, = ax1.plot((1-np.abs(A))*t*1, t*0, color='red', linewidth=4) line4, = ax3.plot((np.abs(A)-1)*t, t*0, color='red', linewidth=4) point1 = ax1.scatter(1-np.abs(A), 0, linewidth=5, color='red') point2 = ax3.scatter(np.abs(A)-1, 0, linewidth=5, color='red') line5, = ax2.plot(0*t, G[0]*t, color='red', linewidth=4) line6, = ax4.plot(0*t, G2[0]*t, color='red', linewidth=4) point3 = ax2.scatter(0, G[0], color='red', linewidth=5) point4 = ax4.scatter(0, G2[0], color='red', linewidth=5) # In[5]: n_frames = 55 def update(i): t0 = i*1./n_frames B = [a_mod*np.cos(2*np.pi*t0), -a_mod*np.sin(2*np.pi*t0)] line1.set_xdata(1-t*B[0]) line1.set_ydata(-t*B[1]) C = [np.cos(2*np.pi*t0), -np.sin(2*np.pi*t0)] line2.set_xdata(np.abs(A)-t*C[0]) line2.set_ydata(-t*C[1]) line3.set_xdata((1-B[0])*t) line3.set_ydata(-t*B[1]) line4.set_xdata((np.abs(A)-C[0])*t) line4.set_ydata(-t*C[1]) point1.set_offsets((1-B[0], -B[1])) point2.set_offsets((np.abs(A)-C[0], -C[1])) line5.set_xdata(2*np.pi*t0+0*t) line6.set_xdata(2*np.pi*t0+0*t) Z0 = np.cos(2*np.pi*t0) - 1j*np.sin(2*np.pi*t0) G0 = np.angle(1-A*Z0) G20 = np.angle(1-np.conj(Ainv)*Z0) line5.set_ydata(G0*t) line6.set_ydata(G20*t) point3.set_offsets((2*np.pi*t0, G0)) point4.set_offsets((2*np.pi*t0, G20)) return line1, line2, line3, line4, point1, point2, line5, line6, point3, point4 # In[ ]: anim = FuncAnimation(fig, update, frames=np.arange(0,n_frames), interval=50, blit=True) if(createGif): anim.save('result.gif', dpi=30, writer='imagemagick') else: pl.show() # In[ ]: