Statistical tests

Whitenoise check

PyEMD.checks.whitenoise_check(IMFs: numpy.ndarray, test_name: str = 'aposteriori', rescaling_imf: int = 1, alpha: float = 0.95)[source]

Whitenoise statistical significance test.

Performs whitenoise test as described by Wu & Huang [Wu2004].

Parameters
IMFs: np.ndarray

(Required) numpy array containing IMFs computed from a normalized signal

test_name: str

(Optional) Test type. Supported values: ‘apriori’, ‘aposteriori’. (default ‘aposteriori’)

rescaling_imf: int

(Optional) ith IMF of the signal used in rescaling for ‘a posteriori’ test. (default 1)

alpha: float

(Optional) The percentiles at which the test is to be performed; 0 < alpha < 1; (default 0.95)

Returns
Optional dictionary

Returns dictionary with keys and values as IMFs’ number and test result, respetively, Test results can be either 0 (fail) or 1 (pass). In case of problems with the input imfs, e.g. NaN values or no imfs, we return None.

References

Wu2004

Zhaohua Wu, and Norden E. Huang. “A Study of the Characteristics of White Noise Using the Empirical Mode Decomposition Method.” Proceedings: Mathematical, Physical and Engineering Sciences, vol. 460, no. 2046, The Royal Society, 2004, pp. 1597–611, http://www.jstor.org/stable/4143111.

Examples

>>> import numpy as np
>>> from PyEMD import EMD
>>> from PyEMD.checks import whitenoise_check
>>> T = np.linspace(0, 1, 100)
>>> S = np.sin(2*2*np.pi*T)
>>> emd = EMD()
>>> imfs = emd(S)
>>> significant_imfs = whitenoise_check(imfs, test_name='apriori')
>>> significant_imfs
{1: 1, 2: 1}
>>> type(significant_imfs)
<class 'dict'>