8000 Changed normalization in _spectral_helper() to obtain conistent scaling by DietBru · Pull Request #8582 · matplotlib/matplotlib · GitHub
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Changed normalization in _spectral_helper() to obtain conistent scaling #8582

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Jun 12, 2017
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Changed normalization in _spectral_helper() to obtain conistent scaling #8582

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Changed normalization in _spectral_helper() to obtain conistent scali…
DietBru May 6, 2017
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Added note to api_changes
DietBru Jun 11, 2017
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Added note to api_changes
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DietBru committed Jun 11, 2017
commit ee1c40dd94b5dae8f95a1582bee7dc4d3aaf223e
31 changes: 31 additions & 0 deletions doc/api/api_changes/2017-06-11-DB_magnitude_spectrum.rst
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Correct scaling of :func:`magnitude_spectrum()`
```````````````````````````````````````````````

The functions :func:`matplotlib.mlab.magnitude_spectrum()` and :func:`matplotlib.pyplot.magnitude_spectrum()` implicitly assumed the sum
of windowing function values to be one. In Matplotlib and Numpy the
standard windowing functions are scaled to have maximum value of one,
which usually results in a sum of the order of n/2 for a n-point
signal. Thus the amplitude scaling :func:`magnitude_spectrum()` was
off by that amount when using standard windowing functions (`Bug 8417
<https://github.com/matplotlib/matplotlib/issues/8417>`_ ). Now the
behavior is consistent with :func:`matplotlib.pyplot.psd()` and
:func:`scipy.signal.welch()`. The following example demonstrates the
new and old scaling::

import matplotlib.pyplot as plt
import numpy as np

tau, n = 10, 1024 # 10 second signal with 1024 points
T = tau/n # sampling interval
t = np.arange(n)*T

a = 4 # amplitude
x = a*np.sin(40*np.pi*t) # 20 Hz sine with amplitude a

# New correct behavior: Amplitude at 20 Hz is a/2
plt.magnitude_spectrum(x, Fs=1/T, sides='onesided', scale='linear')

# Original behavior: Amplitude at 20 Hz is (a/2)*(n/2) for a Hanning window
w = np.hanning(n) # default window is a Hanning window
plt.magnitude_spectrum(x*np.sum(w), Fs=1/T, sides='onesided', scale='linear')

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