Radboud University and Radboud University Medical Center, Donders Institute for Neuroscience, the Netherlands.
Neuroimage. 2019 Oct 1;199:81-86. doi: 10.1016/j.neuroimage.2019.05.048. Epub 2019 May 27.
Complex 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 spectral 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 (expressed as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and can facilitate proper analyses, reporting, and interpretation of results. MATLAB code and sample data are provided.
复 Morlet 小波常用于分析非平稳时间序列数据的时频，例如从大脑中记录的神经电信号。Morlet 小波的关键参数是使正弦波变细的高斯的宽度。该宽度参数控制时间精度和频谱精度之间的权衡。它通常定义为“周期数”，但此参数不透明，并且通常会导致不确定性和次优的分析选择，并且难以解释和评估。本文的目的是提出 Morlet 小波在时间和频率上的替代公式，这些公式可以根据所需的时间和频谱平滑度（以半最大值全宽表示）直接对小波进行参数化。这种表示形式提供了对重要数据分析参数的清晰认识，并可以促进正确的分析，报告和结果解释。提供了 MATLAB 代码和示例数据。
