A better way to define and describe Morlet wavelets for time-frequency analysis

By Michael X. Cohen. bioRxiv, 2018

408 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Control and Systems Engineering, Signal Processing

View Paper: https://www.semanticscholar.org/paper/636bc2ae5c7b6d8ae536952590b1c6823294a2d4

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Citations in the corpus

Intracranial recordings reveal high-frequency activity in the human temporal-parietal cortex supporting non-literal language processing (2024, methodology): “For that, we estimated time-frequency representations (TFRs) using complex Morlet wavelet convolution (Cohen, 2019) for each trial excluding artifactual periods as described above.”
The Role of Fronto‐Central Theta Oscillations in Inter‐Sensory Selective Attention (2025, unknown): “TF was computed using a set of complex Morlet wavelets: w (t,f) = Ae − t 2 ∕ 2 σ 2t e 2 𝜋 ft (Cohen 2019).”
Strengthening of alpha synchronization is a neural correlate of cognitive transfer (2024, methodology): “The transformation was done using MNE-python (Cohen 2019).”
Aging impairs primary task resumption and attentional control processes following interruptions (2021, background): “The tapering Gaussian was designed with a full width at half maximum (FWHM, Cohen, 2019) of 2.75 in the frequency domain and 298 in the time domain.”