Wavelets: Cone of Influence

by MednataMiza
Tags: signal processing, wavelet, wavelet transform, wavelets
MednataMiza is offline
Sep19-13, 06:59 AM
P: 44
While reading this paper I came across the term Cone of Influence which is described as

COI is the region of the wavelet spectrum in which edge effects become important
and is defined here as the e-folding time for the autocorrelation of wavelet
power at each scale.
As an example: We have a vector with length 1001 and then compress it using the Mexican Hat Wavelet. As a result we get the following power spectrum plot:

Then using this tool we obtain the same power spectrum, but with the COI added (cross-hatched region on plot b).

Usually the coefficients of a CWT are presented in the timescale {b, a} half plane with linear scale on time b axis, pointing to the right, and logarithmic scale а axis, facing downward with increasing octave. To resolve localized signals, the analyzing wavelet ψ(t) is chosen so that it vanishes outside some interval (t_min, t_max). In this case the domain in the {b,a} half plane that can be influenced by a point (b_0, a_0) mainly lies within the cone of influence defined by
Abs[b - b_0] = a Sqrt[2]
My question is: Using the above equation how should I plot the COI ? What I mean is how should I choose a, b and b_0 with respect to the wavelet used in the transform ?
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