Wavelets: Cone of Influence

  1. While reading this paper I came across the term Cone of Influence which is described as

    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:
    [​IMG]

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

    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
    Code (Text):
    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 ?
     
  2. jcsd
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