def compute_spectrum_welch(sig,
fs,
avg_type='mean',
window='hann',
nperseg=None,
noverlap=None,
f_range=None,
outlier_percent=None):
"""Compute the power spectral density using Welch's method.
Parameters
-----------
sig : 1d or 2d array
Time series.
fs : float
Sampling rate, in Hz.
avg_type : {'mean', 'median'}, optional
Method to average across the windows:
* 'mean' is the same as Welch's method, taking the mean across FFT windows.
* 'median' uses median across FFT windows instead of the mean, to minimize outlier effect.
window : str or tuple or array_like, optional, default: 'hann'
Desired window to use. See scipy.signal.get_window for a list of available windows.
If array_like, the array will be used as the window and its length must be nperseg.
nperseg : int, optional
Length of each segment, in number of samples.
If None, and window is str or tuple, is set to 1 second of data.
If None, and window is array_like, is set to the length of the window.
noverlap : int, optional
Number of points to overlap between segments.
If None, noverlap = nperseg // 8.
f_range : list of [float, float] optional
Frequency range to sub-select from the power spectrum.
outlier_percent : float, optional
The percentage of outlier values to be removed. Must be between 0 and 100.
Returns
-------
freqs : 1d array
Frequencies at which the measure was calculated.
spectrum : 1d or 2d array
Power spectral density.
"""
# Calculate the short time fourier transform with signal.spectrogram
nperseg, noverlap = check_spg_settings(fs, window, nperseg, noverlap)
freqs, _, spg = spectrogram(sig, fs, window, nperseg, noverlap)
# Throw out outliers if indicated
if outlier_percent is not None:
spg = discard_outliers(spg, outlier_percent)
# Average across windows
spectrum = get_avg_func(avg_type)(spg, axis=-1)
# Trim spectrum, if requested
if f_range:
freqs, spectrum = trim_spectrum(freqs, spectrum, f_range)
return freqs, spectrum
def compute_spectrum_welch(sig, fs, avg_type='mean', window='hann',
nperseg=None, noverlap=None,
f_range=None, outlier_percent=None):
"""Compute the power spectral density using Welch's method.
Parameters
----------
sig : 1d or 2d array
Time series.
fs : float
Sampling rate, in Hz.
avg_type : {'mean', 'median'}, optional
Method to average across the windows:
* 'mean' is the same as Welch's method, taking the mean across FFT windows.
* 'median' uses median across FFT windows instead of the mean, to minimize outlier effects.
window : str or tuple or array_like, optional, default: 'hann'
Desired window to use. See scipy.signal.get_window for a list of available windows.
If array_like, the array will be used as the window and its length must be nperseg.
nperseg : int, optional
Length of each segment, in number of samples.
If None, and window is str or tuple, is set to 1 second of data.
If None, and window is array_like, is set to the length of the window.
noverlap : int, optional
Number of points to overlap between segments.
If None, noverlap = nperseg // 8.
f_range : list of [float, float], optional
Frequency range to sub-select from the power spectrum.
outlier_percent : float, optional
The percentage of outlier values to be removed. Must be between 0 and 100.
Returns
-------
freqs : 1d array
Frequencies at which the measure was calculated.
spectrum : 1d or 2d array
Power spectral density.
Notes
-----
- Welch's method ([1]_) computes a power spectra by averaging over windowed FFTs.
References
----------
.. [1] Welch, P. (1967). The use of fast Fourier transform for the estimation of power
spectra: A method based on time averaging over short, modified periodograms.
IEEE Transactions on Audio and Electroacoustics, 15(2), 70–73.
DOI: https://doi.org/10.1109/TAU.1967.1161901
Examples
--------
Compute the power spectrum of a simulated time series using Welch's method:
>>> from neurodsp.sim import sim_combined
>>> sig = sim_combined(n_seconds=10, fs=500,
... components={'sim_powerlaw': {}, 'sim_oscillation': {'freq': 10}})
>>> freqs, spec = compute_spectrum_welch(sig, fs=500)
"""
# Calculate the short time Fourier transform with signal.spectrogram
nperseg, noverlap = check_spg_settings(fs, window, nperseg, noverlap)
freqs, _, spg = spectrogram(sig, fs, window, nperseg, noverlap)
# Throw out outliers if indicated
if outlier_percent is not None:
spg = discard_outliers(spg, outlier_percent)
# Average across windows
spectrum = get_avg_func(avg_type)(spg, axis=-1)
# Trim spectrum, if requested
if f_range:
freqs, spectrum = trim_spectrum(freqs, spectrum, f_range)
return freqs, spectrum