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
    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.
    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
    For futher details, see Lilly (2017).
    'morseregion --f' generates a sample figure.
    Usage: [t,f]=morseregion(A,ga,be,fo);
    This is part of JLAB --- type 'help jlab' for more information
    (C) 2006--2017 J.M. Lilly --- type 'help jlab_license' for details

contents | allhelp | index