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Cleanup psd example. #23426

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71 changes: 22 additions & 49 deletions examples/lines_bars_and_markers/psd_demo.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
"""
========
Psd Demo
PSD Demo
========

Plotting Power Spectral Density (PSD) in Matplotlib.
Expand All @@ -9,13 +9,12 @@
many useful libraries for computing a PSD. Below we demo a few examples
of how this can be accomplished and visualized with Matplotlib.
"""

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.mlab as mlab
import matplotlib.gridspec as gridspec

# Fixing random state for reproducibility
np.random.seed(19680801)
np.random.seed(19680801) # Fix random state for reproducibility.

dt = 0.01
t = np.arange(0, 10, dt)
Expand All @@ -30,8 +29,6 @@
ax0.plot(t, s)
ax1.psd(s, 512, 1 / dt)

plt.show()

###############################################################################
# Compare this with the equivalent Matlab code to accomplish the same thing::
#
Expand All @@ -57,43 +54,35 @@
y = 10. * np.sin(2 * np.pi * 4 * t) + 5. * np.sin(2 * np.pi * 4.25 * t)
y = y + np.random.randn(*t.shape)

# Plot the raw time series
# Plot the raw time series.
fig = plt.figure(constrained_layout=True)
gs = gridspec.GridSpec(2, 3, figure=fig)
gs = fig.add_gridspec(2, 3)
ax = fig.add_subplot(gs[0, :])
ax.plot(t, y)
ax.set_xlabel('time [s]')
ax.set_ylabel('signal')
ax.set(xlabel='time [s]', ylabel='signal')

# Plot the PSD with different amounts of zero padding. This uses the entire
# time series at once
# time series at once.
ax2 = fig.add_subplot(gs[1, 0])
ax2.psd(y, NFFT=len(t), pad_to=len(t), Fs=fs)
ax2.psd(y, NFFT=len(t), pad_to=len(t) * 2, Fs=fs)
ax2.psd(y, NFFT=len(t), pad_to=len(t) * 4, Fs=fs)
ax2.set_title('zero padding')
ax2.set(title='zero padding')

# Plot the PSD with different block sizes, Zero pad to the length of the
# Plot the PSD with different block sizes, zero pad to the length of the
# original data sequence.
ax3 = fig.add_subplot(gs[1, 1], sharex=ax2, sharey=ax2)
ax3.psd(y, NFFT=len(t), pad_to=len(t), Fs=fs)
ax3.psd(y, NFFT=len(t) // 2, pad_to=len(t), Fs=fs)
ax3.psd(y, NFFT=len(t) // 4, pad_to=len(t), Fs=fs)
ax3.set_ylabel('')
ax3.set_title('block size')
ax3.set(ylabel='', title='block size')

# Plot the PSD with different amounts of overlap between blocks
# Plot the PSD with different amounts of overlap between blocks.
ax4 = fig.add_subplot(gs[1, 2], sharex=ax2, sharey=ax2)
ax4.psd(y, NFFT=len(t) // 2, pad_to=len(t), noverlap=0, Fs=fs)
ax4.psd(y, NFFT=len(t) // 2, pad_to=len(t),
noverlap=int(0.05 * len(t) / 2.), Fs=fs)
ax4.psd(y, NFFT=len(t) // 2, pad_to=len(t),
noverlap=int(0.2 * len(t) / 2.), Fs=fs)
ax4.set_ylabel('')
ax4.set_title('overlap')

plt.show()

ax4.psd(y, NFFT=len(t) // 2, pad_to=len(t), Fs=fs, noverlap=0)
ax4.psd(y, NFFT=len(t) // 2, pad_to=len(t), Fs=fs, noverlap=int(0.025*len(t)))
ax4.psd(y, NFFT=len(t) // 2, pad_to=len(t), Fs=fs, noverlap=int(0.1*len(t)))
ax4.set(ylabel='', title='overlap')

###############################################################################
# This is a ported version of a MATLAB example from the signal
Expand All @@ -115,22 +104,14 @@

ax0.psd(xn, NFFT=301, Fs=fs, window=mlab.window_none, pad_to=1024,
scale_by_freq=True)
ax0.set_title('Periodogram')
ax0.set_yticks(yticks)
ax0.set_xticks(xticks)
ax0.set(title='Periodogram', xticks=xticks, yticks=yticks, ylim=yrange)
ax0.grid(True)
ax0.set_ylim(yrange)

ax1.psd(xn, NFFT=150, Fs=fs, window=mlab.window_none, pad_to=512, noverlap=75,
scale_by_freq=True)
ax1.set_title('Welch')
ax1.set_xticks(xticks)
ax1.set_yticks(yticks)
ax1.set_ylabel('') # overwrite the y-label added by `psd`
ax1.set(title='Welch', xticks=xticks, yticks=yticks, ylim=yrange,
ylabel='') # overwrite the y-label added by `psd`
ax1.grid(True)
ax1.set_ylim(yrange)

plt.show()

###############################################################################
# This is a ported version of a MATLAB example from the signal
Expand All @@ -139,13 +120,11 @@
#
# It uses a complex signal so we can see that complex PSD's work properly.

prng = np.random.RandomState(19680801) # to ensure reproducibility

fs = 1000
t = np.linspace(0, 0.3, 301)
A = np.array([2, 8]).reshape(-1, 1)
f = np.array([150, 140]).reshape(-1, 1)
xn = (A * np.exp(2j * np.pi * f * t)).sum(axis=0) + 5 * prng.randn(*t.shape)
xn = (A * np.exp(2j * np.pi * f * t)).sum(0) + 5 * np.random.randn(*t.shape)

fig, (ax0, ax1) = plt.subplots(ncols=2, constrained_layout=True)

Expand All @@ -155,19 +134,13 @@

ax0.psd(xn, NFFT=301, Fs=fs, window=mlab.window_none, pad_to=1024,
scale_by_freq=True)
ax0.set_title('Periodogram')
ax0.set_yticks(yticks)
ax0.set_xticks(xticks)
ax0.set(title='Periodogram', xticks=xticks, yticks=yticks, ylim=yrange)
ax0.grid(True)
ax0.set_ylim(yrange)

ax1.psd(xn, NFFT=150, Fs=fs, window=mlab.window_none, pad_to=512, noverlap=75,
scale_by_freq=True)
ax1.set_title('Welch')
ax1.set_xticks(xticks)
ax1.set_yticks(yticks)
ax1.set_ylabel('') # overwrite the y-label added by `psd`
ax1.set(title='Welch', xticks=xticks, yticks=yticks, ylim=yrange,
ylabel='') # overwrite the y-label added by `psd`
ax1.grid(True)
ax1.set_ylim(yrange)

plt.show()