Plot the phase spectrum in Python using Matplotlib

A Signal is an electromagnetic field or an electric current to transmit data. There are various components of a signal such as frequency, amplitude, wavelength, phase, angular frequency and period from which it is described.
A periodic signal can be represented using the below sine function:

y = A sin(w*t + Q)

In which A represents the amplitude(in meter), w represents frequency(in hertz), t represents time period(in seconds) and Q represents phase(in radian) of the periodic signal.

The two major components frequency and phase of a periodic signal define the Phase Spectrum of that signal. The frequency components of the periodic signal are plotted in the horizontal axis and phase component of the periodic signal is plotted in the vertical axis.

In Python, the phase_spectrum() method in the pyplot module of Python matplotlib library plots the phase spectrum of a periodic signal. Below are some programs which demonstrate the use of phase_spectrum() method to visualize the phase spectrum of different periodic signals.
Example 1:

filter_none

edit
close

play_arrow

link
brightness_4
code

# importing modules
import numpy
from matplotlib import pyplot 
   
# assigning time values of the signal
# initial time period, final time period and phase angle
signalTime = numpy.arange(5, 10, 0.25);
  
# getting the amplitude of the signal
signalAmplitude = numpy.sin(signalTime)
  
# plotting the signal 
pyplot.plot(signalTime, signalAmplitude, color ='green')
pyplot.show()
  
pyplot.xlabel('Time')
pyplot.ylabel('Amplitude')
pyplot.title("Signal")
  
  
# plotting the phase spectrum of the signal 
pyplot.phase_spectrum(signalAmplitude, color ='green')
  
pyplot.title("Phase Spectrum of the Signal")
pyplot.show()

chevron_right


Output:


The first graph represent the signal in Amplitude vs Time components, the second graph represents the phase spectrum of the signal in Phase vs Frequency graph by using phase_spectrum() on the signal having time period from 5 to 10 seconds, 0.25 radian phase angle, frequency of the signal is calculated from the given time period and amplitude of the signal is calculated using the sin() function in numpy module.
Example 2:



filter_none

edit
close

play_arrow

link
brightness_4
code

# importing modules
import numpy
from matplotlib import pyplot 
   
# assigning time values of the signal
# initial time period, final time period and phase angle
signalTime = numpy.arange(0, 1, 0.1)
  
# getting the amplitude of the signal
signalAmplitude = numpy.sin(signalTime)
  
# plotting the signal 
pyplot.plot(signalTime, signalAmplitude, color ='green')
pyplot.show()
  
pyplot.xlabel('Time')
pyplot.ylabel('Amplitude')
pyplot.title("Signal")
  
  
# plotting the phase spectrum of the signal 
pyplot.phase_spectrum(signalAmplitude, color ='green')
  
pyplot.title("Phase Spectrum of the Signal")
pyplot.show()

chevron_right


Output:


In the above program, as the amplitude of the signal is increasing with time so a sinusoidal wave is not formed in the first graph. The signal exists in the time period of 0 to 1 second and the phase angle is 0.1 radian, the phase spectrum of the signal is depicted using phase_spectrum() method.

Example 3:

filter_none

edit
close

play_arrow

link
brightness_4
code

# importing modules
import numpy
from matplotlib import pyplot 
   
# assigning time values of the signal
# initial time period, final time period and phase angle 
signalTime = numpy.arange(1, 100, 0.5);
  
# getting the amplitude of the signal
signalAmplitude = numpy.sin(signalTime)
  
# plotting the signal 
pyplot.plot(signalTime, signalAmplitude, color ='green')
pyplot.show()
  
pyplot.xlabel('Time')
pyplot.ylabel('Amplitude')
pyplot.title("Signal")
  
  
# plotting the phase spectrum of the signal 
pyplot.phase_spectrum(signalAmplitude, color ='green')
  
pyplot.title("Phase Spectrum of the Signal")
pyplot.show()

chevron_right


Output:


Here, the signal is represented in Amplitude vs Time graph which forms sinusoidal waves and the phase spectrum of the signal is represented using phase_spectrum() method in Phase vs Frequency graph. The time period of the signal starts from 1 second to 100th second and the phase angle is 0.5 radian.




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.


Article Tags :

Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.