emd.imftools.assess_harmonic_criteria#

emd.imftools.assess_harmonic_criteria(IP, IF, IA, num_segments=None, base_imf=None, print_result=True)[source]#

Assess IMFs for potential harmonic relationships.

This function implements tests for the criteria defining when signals can be considered ‘harmonically related’ as introduced in [1]. Broadly, harmonically related signals are defined as having an integer frequency ratio, constant phase relationship, and a well-defined joint instantaneous frequency

Three criteria are assessed by splitting the time-series into approximately equally sized segments and computing metrics within each segment.

Parameters:
IP, IF, IAndarray of equal shape

Instantaneous Phase, Frequency and Amplitude estimates for a set of IMFs. These are typically the outputs from emd.spectra.frequency_transform.

num_segmentsint

Number of segments to split the time series into to enable statistical assessment.

base_infint

Index of IMF to be considered the potential ‘fundamental’ oscillation.

print_resultbool

Flag indicating whether to print a summary table of results.

Returns:
df

Pandas DataFrame containing a range of summary and comparison metrics.

Notes

In detail, this function compares each IMF to a ‘base’ IMF to see if it can be considered a potential harmonic. Each pair of IMFs are assessed for:

1) An integer frequency ratio. The distribution of frequency ratios across segments is compared to its closest integer value with a 1-sample t-test

2) Consistent phase relationship. The instantaneous phase time-courses are assessed for temporal dependence using a Distance Correlation t-statistic.

3) The af ratio is less than 1. The product of the amplitude ratio and frequency ratio of the two IMFs should be less than 1 according to a 1-sided 1-sample t-test.

References

[1]

Fabus, M. S., Woolrich, M. W., Warnaby, C. W., & Quinn, A. J. (2022). Understanding Harmonic Structures Through Instantaneous Frequency. IEEE Open Journal of Signal Processing. doi: 10.1109/OJSP.2022.3198012.