MATLAB: Wavelet Coherence: S smoothing operator

Question

I am using the wavelet coherence function on physiological data, from the wavelet toolbox. Overall, I am getting the result I want, but I would like to know how is the smoothing operator in time and scale S in the wavelet coherence function defined?

In particular, there are two references Grinsted et al., 2004 and also Torrence and Webster, 1999, which have a definition for the smoothing operator. To my understanding that is a window moving average in time and scale, but I would like to know, does anyone know how it is defined in the matlab function "wcoherence(x,y)".

Many thanks!

Answer 1

In wcoherence, smoothing is done by calculating weighted running average (or convolution) in both the time and scale directions. Taking reference from Torrence and Webster, smoothing operator in wcoherence function is given by