An O(n) algorithm for clipping wide peaks from 1D signals, designed for application to removing harmonic artefacts from the continuous wavelet transform.

Published in the open-access article: https://www.frontiersin.org/articles/10.3389/fphys.2020.00484/full

Given a signal with amplitudes y[0..n-1] and non-decreasing locations x[0..n-1], clips all peaks that are too wide x[b] - x[a] > k for all b > a and given parameter k.

The following animation shows an example with a uniformally increasing x along the horizontal, y along the vertical, and k = 12:

The mesaclip.py file contains the main algorithm in the mesaclip function, and demo.py will reproduce the animation. Running the mesaclip.py file will run tests on random signals.

The following table shows four examples comparing a convential continuous wavelet transform and one with mesaclipping applied. The middle subplots use a conventional Morse(β=12, γ=3) wavelet transform, and the bottom subplots use a Morse(β=1.58174, γ=3) wavelet with mesaclipping applied. The mesaclipped version does not suffer from harmonic artefacts generated due to sharp changes in the singals.

From a smooth to a spiky signal	Bursts of Dirac deltas
Thresholded chirp	Real EMG signal

The choice of β=1.58174 is based on minimising the 1st harmonic amplitude of a Dirac comb halfway between two Dirac delta functions:

Example applications to some real EMG data:

Exploration of signal-to-noise ratio for artificial spike-train signals of varying regularity:

Estimates of the ground truth frequency: