Just for the record, please skip it.
Article Directory
Directly upload the code, the program can be run directly
Master filea9.py
import numpy as np
import matplotlib.pyplot as plt
import a9mysubplot
from sklearn.decomposition import FastICA
ts=0.005
t=np.arange(0,1,ts)
s1=np.sin(2*np.pi*80*t);s2=np.sin(2*np.pi*20*t);s2=np.array(20 * (5 * [2] + 5 * [-2]));a9mysubplot.mysubplot([s1,s2])
def fftspectrum(thesignal,fs): # add fs
nsel=thesignal.size
fsel=fs*(np.arange(0,nsel/2)/nsel) # add fs*
ysel=np.fft.fft(thesignal)
ysel=np.abs(ysel)
ysel=ysel[0:len(fsel)]
# ysel=20*np.log(ysel)
# plt.figure()
plt.plot(fsel,ysel)
# plt.show()
fftspectrum(s1,1/ts)
plt.show()
stack=np.array([[0.5,0.5],[0.3,0.7]]);mix=stack.dot([s1,s2]);a9mysubplot.mysubplot([mix[0,:],mix[1,:]])
ica=FastICA(n_components=2)
spro=(ica.fit_transform(mix.T)).T;a9mysubplot.mysubplot([spro[0,:],spro[1,:]])
def fftspectrum(thesignal,fs): # add fs
nsel=thesignal.size
fsel=fs*(np.arange(0,nsel/2)/nsel) # add fs*
ysel=np.fft.fft(thesignal)
ysel=np.abs(ysel)
ysel=ysel[0:len(fsel)]
# ysel=20*np.log(ysel)
# plt.figure()
plt.plot(fsel,ysel)
# plt.show()
fftspectrum(spro[0,:],1/ts)
plt.show()
The function for drawing multiple graphs is written in a new file a9mysubplot:
import matplotlib.pyplot as plt
def mysubplot(file):
l=len(file)
if l==2:
plt.figure()
plt.subplot(211);plt.plot(file[0])
plt.subplot(212);plt.plot(file[1])
if l==3:
plt.figure()
plt.subplot(311);plt.plot(file[0])
plt.subplot(312);plt.plot(file[1])
plt.subplot(313);plt.plot(file[2])
if l==4:
plt.figure()
plt.subplot(411);plt.plot(file[0])
plt.subplot(412);plt.plot(file[1])
plt.subplot(413);plt.plot(file[2])
plt.subplot(414);plt.plot(file[3])
if l==6:
plt.figure()
plt.subplot(611);plt.plot(file[0])
plt.subplot(612);plt.plot(file[1])
plt.subplot(613);plt.plot(file[2])
plt.subplot(614);plt.plot(file[3])
plt.subplot(615);plt.plot(file[4])
plt.subplot(616);plt.plot(file[5])
if l==8:
plt.figure()
plt.subplot(811);plt.plot(file[0])
plt.subplot(812);plt.plot(file[1])
plt.subplot(813);plt.plot(file[2])
plt.subplot(814);plt.plot(file[3])
plt.subplot(815);plt.plot(file[4])
plt.subplot(816);plt.plot(file[5])
plt.subplot(817);plt.plot(file[6])
plt.subplot(818);plt.plot(file[7])
plt.show()
Put a9.py and a9mysubplot.py in the same folder and run the a9.pyfile
The results show that
The blogger found that Python FastICAcan’t separate the mixed signals of two sinusoidal signals; therefore, set an original signal s1 as a sinusoidal signal and s2 as a square wave signal.
original signal
The frequency spectrum of the sinusoidal signal in the original signal
Two sine square wave signals mixed with (5,5) weight and (3,7) weight respectively
FastICA unmixed signal
It is found to be exactly the same as the original signal; but sometimes the unmixed sine wave in the picture is below, and sometimes it is drawn on top
Observe the signal spectrum after unmixing (especially the spectrum of a sine wave)
It is found that the frequency is still 80Hz;
This picture is the frequency spectrum of a square wave
reference
Thanks to the big blogger for the article
Portal
The blogger modified the code of the blogger’s blog post,
Can run directly:
import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import FastICA
C = 200
x = np.arange(C)
a = np.linspace(-2, 2, 25)
s1 = np.array([a, a, a, a, a, a, a, a]).reshape(200, )
s2 = 2 * np.sin(0.02 * np.pi * x)
s3 = np.array(20 * (5 * [2] + 5 * [-2]))
ax1 = plt.subplot(311)
ax2 = plt.subplot(312)
ax3 = plt.subplot(313)
ax1.plot(x,s1)
ax2.plot(x,s2)
ax3.plot(x,s3)
plt.show()
s=np.array([s1,s2,s3])
ran=2*np.random.random([3,3])
mix=ran.dot(s)
ax1 = plt.subplot(311)
ax2 = plt.subplot(312)
ax3 = plt.subplot(313)
ax1.plot(x,mix[0,:])
ax2.plot(x,mix[1,:])
ax3.plot(x,mix[2,:])
plt.show()
ica = FastICA(n_components=3)
mix = mix.T
u = ica.fit_transform(mix)
u = u.T
ax1 = plt.subplot(311)
ax2 = plt.subplot(312)
ax3 = plt.subplot(313)
ax1.plot(x,u[0,:])
ax2.plot(x,u[1,:])
ax3.plot(x,u[2,:])
plt.show()
