welch (pyleoclim.utils.spectral.welch)¶

pyleoclim.utils.spectral.welch(ys, ts, window='hann', nperseg=None, noverlap=None, nfft=None, return_onesided=True, detrend=None, sg_kwargs=None, gaussianize=False, standardize=False, scaling='density', average='mean')[source]¶

Estimate power spectral density using Welch’s method

Wrapper for the function implemented in scipy.signal.welch See https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.welch.html for details.

Welch’s method is an approach for spectral density estimation. It computes an estimate of the power spectral density by dividing the data into overlapping segments, computing a modified periodogram for each segment and averaging the periodograms.

Parameters

ys (array) – a time series
ts (array) – time axis of the time series
window (string or tuple) –
Desired window to use. Possible values:
boxcar

triang

blackman

hamming

hann (default)

bartlett

flattop

parzen

bohman

blackmanharris

nuttail

barthann

kaiser (needs beta)

gaussian (needs standard deviation)

general_gaussian (needs power, width)

slepian (needs width)

dpss (needs normalized half-bandwidth)

chebwin (needs attenuation)

exponential (needs decay scale)

tukey (needs taper fraction)
If the window requires no parameters, then window can be a string. If the window requires parameters, then window must be a tuple with the first argument the string name of the window, and the next arguments the needed parameters. If window is a floating point number, it is interpreted as the beta parameter of the kaiser window.
npersegint
Length of each segment. If none, nperseg=len(ys)/2. Default to None This will give three segments with 50% overlap

noverlapint
Number of points to overlap. If None, noverlap=nperseg//2. Defaults to None, represents 50% overlap

nfft: int
Length of the FFT used, if a zero padded FFT is desired. If None, the FFT length is nperseg

return_onesidedbool
If True, return a one-sided spectrum for real data. If False return a two-sided spectrum. Defaults to True, but for complex data, a two-sided spectrum is always returned.

detrendstr
If None, no detrending is applied. Available detrending methods:
None - no detrending will be applied (default);

linear - a linear least-squares fit to ys is subtracted;

constant - the mean of ys is subtracted

savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.

emd - Empirical mode decomposition
sg_kwargsdict
The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.

gaussianizebool
If True, gaussianizes the timeseries

standardizebool
If True, standardizes the timeseries

scaling{“density,”spectrum}
Selects between computing the power spectral density (‘density’) where Pxx has units of V**2/Hz and computing the power spectrum (‘spectrum’) where Pxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’

average{‘mean’,’median’}
Method to use when averaging periodograms. Defaults to ‘mean’.

Returns

res_dict – the result dictionary, including - freq (array): the frequency vector - psd (array): the spectral density vector

Return type

dict