8000 Merge pull request #8582 from vollbier/magnitude_spectrumScaling · matplotlib/matplotlib@aec1e5b · GitHub
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Merge pull request #8582 from vollbier/magnitude_spectrumScaling
API: Changed normalization in _spectral_helper() to obtain consistent scaling
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‎doc/api/api_changes/2017-06-11-DB_magnitude_spectrum.rst

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Correct scaling of :func:`magnitude_spectrum()`
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```````````````````````````````````````````````
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The functions :func:`matplotlib.mlab.magnitude_spectrum()` and :func:`matplotlib.pyplot.magnitude_spectrum()` implicitly assumed the sum
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of windowing function values to be one. In Matplotlib and Numpy the
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standard windowing functions are scaled to have maximum value of one,
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which usually results in a sum of the order of n/2 for a n-point
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signal. Thus the amplitude scaling :func:`magnitude_spectrum()` was
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off by that amount when using standard windowing functions (`Bug 8417
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<https://github.com/matplotlib/matplotlib/issues/8417>`_ ). Now the
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behavior is consistent with :func:`matplotlib.pyplot.psd()` and
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:func:`scipy.signal.welch()`. The following example demonstrates the
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new and old scaling::
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import matplotlib.pyplot as plt
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import numpy as np
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tau, n = 10, 1024 # 10 second signal with 1024 points
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T = tau/n # sampling interval
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t = np.arange(n)*T
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a = 4 # amplitude
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x = a*np.sin(40*np.pi*t) # 20 Hz sine with amplitude a
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# New correct behavior: Amplitude at 20 Hz is a/2
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plt.magnitude_spectrum(x, Fs=1/T, sides='onesided', scale='linear')
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# Original behavior: Amplitude at 20 Hz is (a/2)*(n/2) for a Hanning window
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w = np.hanning(n) # default window is a Hanning window
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plt.magnitude_spectrum(x*np.sum(w), Fs=1/T, sides='onesided', scale='linear')
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‎lib/matplotlib/axes/_axes.py

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@@ -6666,8 +6666,7 @@ def magnitude_spectrum(self, x, Fs=None, Fc=None, window=None,
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scale : [ 'default' | 'linear' | 'dB' ]
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The scaling of the values in the *spec*. 'linear' is no scaling.
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'dB' returns the values in dB scale. When *mode* is 'density',
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this is dB power (10 * log10). Otherwise this is dB amplitude
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'dB' returns the values in dB scale, i.e., the dB amplitude
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(20 * log10). 'default' is 'linear'.
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Fc : integer

‎lib/matplotlib/mlab.py

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@@ -727,12 +727,12 @@ def _spectral_helper(x, y=None, NFFT=None, Fs=None, detrend_func=None,
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elif mode == 'psd':
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result = np.conj(result) * result
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elif mode == 'magnitude':
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result = np.abs(result)
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result = np.abs(result) / np.abs(windowVals).sum()
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elif mode == 'angle' or mode == 'phase':
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# we unwrap the phase later to handle the onesided vs. twosided case
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result = np.angle(result)
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elif mode == 'complex':
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pass
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result /= np.abs(windowVals).sum()
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if mode == 'psd':
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‎lib/matplotlib/tests/baseline_images/test_axes/magnitude_spectrum_freqs_dB.png

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‎lib/matplotlib/tests/baseline_images/test_axes/magnitude_spectrum_freqs_linear.png

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‎lib/matplotlib/tests/baseline_images/test_axes/magnitude_spectrum_noise_dB.png

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‎lib/matplotlib/tests/baseline_images/test_axes/magnitude_spectrum_noise_linear.png

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