welch (pyleoclim.utils.welch)

pyleoclim.utils.welch(ys, ts, window='hann', nperseg=None, noverlap=None, nfft=None, return_onesided=True, detrend=None, params=['default', 4, 0, 1], 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

    paramslist

    The paramters for the Savitzky-Golay filters. The first parameter corresponds to the window size (default it set to half of the data) while the second parameter correspond to the order of the filter (default is 4). The third parameter is the order of the derivative (the default is zero, which means only smoothing.)

    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

See also

periodogram()

Estimate power spectral density using a periodogram

mtm()

Retuns spectral density using a multi-taper method

lomb_scargle()

Return the computed periodogram using lomb-scargle algorithm

wwz_psd()

Return the psd of a timeseries using wwz method.

References

  1. Welch, “The use of the fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms”, IEEE Trans. Audio Electroacoust. vol. 15, pp. 70-73, 1967.

Examples

>>> from pyleoclim import utils
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> # Create a signal
>>> time = np.arange(2001)
>>> f = 1/50
>>> signal = np.cos(2*np.pi*f*time)
>>> # Spectral Analysis
>>> res = utils.welch(signal, time)
>>> # plot
>>> fig = plt.loglog(
...           res['freq'],
...           res['psd'])
>>> plt.xlabel('Frequency')
>>> plt.ylabel('PSD')
>>> plt.show()

(Source code, png)

../../_images/welch-1.png