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# Plot the phase spectrum in Python using Matplotlib

• Last Updated : 27 Apr, 2020

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:

 `# 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()`

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:

 `# 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()`

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:

 `# 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()`

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.

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