MORSEREGION is the jWavelet module of jLab.

 MORSEREGION  Generalized Morse wavelet time-frequency concentration region.
 
    MORSEREGION computes two different type of time-frequency concentration
    regions for the generalized Morse wavelets.
 
    This function is part of 'element analysis' described in Lilly (2017), 
    "Element analysis: a wavelet-based method for analyzing time-localized
    events in noisy time series", submitted.  Available at www.jmlilly.net.
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    Localization regions
 
    [T,F]=MORSEREGION(A,GAMMA,BETA,FO) returns the localization region of 
    the generalized Morse wavelets specified by GAMMA and BETA centered on
    *radian* frequency FO.  The nonnegative number A sets the region area.
 
    T and F are then a parametric curve such that PLOT(T,F) shows the shape
    of the time-frequency localization region. 
 
    The localization regions are based on a reconstruction of the signal 
    from a limited inversion region, see Daubechies and Paul (1988) and 
    Olhede and Walden (2002, 2003a) for details.  
  
    Note that the definition of area used here is one-half of that used in
    Olhede and Walden (2002, 2003a), as we only count positive frequencies.
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    Regions of influence
 
    [T,F]=MORSEREGION(LAMBDA,GAMMA,BETA,MU,FRHO) with five input arguments 
    returns the contour at which the energy-normalized wavelet transform of
    another wavelet falls to a fraction LAMBDA of its peak value.
 
    The wavelet we are taking the transform of has parameters GAMMA and MU,
    and is characterized by a scale frequency FRHO.  We then take the 
    wavelet transform of this wavelet with a (GAMMA,BETA) wavelet.  Note
    that this region assumes a 1/S and not a 1/SQRT(S) normalization.
 
    T and F are then a parametric curve such approximating the region where
    this transform takes on a fraction LAMBDA of its peak value.  This 
    approximation is formed analytically through a Taylor series expansion.
 
    Note that FRHO is the frequency of the analyzed wavelet, not the 
    location of the maximum within the transform, which is given by
 
        FO=FRHO*MORSEFREQ(GAMMA,BETA)/MORSEFREQ(GAMMA,MU)*
                                       ((MU+1)./BETA)^(1/GAMMA).
 
    For futher details, see Lilly (2017).
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    'morseregion --f' generates a sample figure.
 
    Usage: [t,f]=morseregion(A,ga,be,fo);
           [t,f]=morseregion(lambda,ga,be,mu,frho);
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    This is part of JLAB --- type 'help jlab' for more information
    (C) 2006--2017 J.M. Lilly --- type 'help jlab_license' for details