RT Journal Article
SR Electronic
T1 A better way to define and describe Morlet wavelets for time-frequency analysis
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 397182
DO 10.1101/397182
A1 Michael X Cohen
YR 2018
UL http://biorxiv.org/content/early/2018/08/21/397182.abstract
AB Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trade-off between temporal precision and frequency precision. It is typically defined as the “number of cycles,” but this parameter is opaque, and often leads to uncertainty and suboptimal analysis choices, as well as being difficult to interpret and evaluate. The purpose of this paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and should facilitate proper analyses, reporting, and interpretation of results. MATLAB code is provided.