TRANSMAX is the jWavelet module of jLab.

  TRANSMAX  Locates modulus maximum points of wavelet transform.
 
    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.
   
    [INDEX,WW,FF]=TRANSMAX(FA,W) gives the indicies INDEX, transform values
    WW, and scale frequencies FF of all the maxima points in time and scale
    of the wavelet transform W, which has been performed at frequencies FS.
 
    W is oriented with time in rows and different scales or frequencies in
    its columns, as output by WAVETRANS.  FS is a length SIZE(W,2) array
    giving the scale frequencies at which the wavelet transform was taken.
  
    The output variables are all column arrays.
 
    TRANSMAX applies a central difference to both rows and columns to 
    locate maxima, then applies a quadratic interpolation in columns to 
    obtain a refined estimate of the scale locations.  The output fields FF 
    and WW represent interpolated values at these refined scale locations.
    
    Note that W can have up to four dimensions.  This is useful for
    datasets containing many replicate time series. Use 
  
            [II,JJ,KK,RR]=IND2SUB(SIZE(W),INDEX)
 
    to convert INDEX into row numbers II, column numbers JJ, and so forth.
 
    TRANSMAX(...,CHI) returns only those maxima points having magnitudes
    exceeding CHI, i.e. ABS(W)>CHI.  CHI may be a scalar, or an array of
    length SIZE(W,2).  In the latter case, different cutoffs are applied 
    to maximum points located in the different columns of W.
    _______________________________________________________________________
 
    Missing data fraction
 
    TRANSMAX can also return a measure of how much each detected transform
    maximum overlaps periods of interpolated or missing data. 
 
    It is sometimes the case that one is interested in transform maxima for
    time series that have missing data points or gaps.  In this case, one
    can just interpolate over all the missing data points, pass the
    interpolated data to TRANSMAX, and then find the missing data fraction.
 
    [INDEX,WW,FF,RR]=TRANSMAX(FS,W,{GAMMA,BETA,BOOL}), where the third 
    input argument is a cell array, returns the missing data fraction RR.  
    Here BOOL is a boolean variable of the same length as the analyzed time
    series, which is true if a datapoint was originally missing.  
  
    If GAMMA and BETA are the parameters of the Morse wavelet used in the
    transform, the wavelet time-domain width at scale frequency FS is
    approximately L=2*SQRT(2)*SQRT(BETA*GAMMA)./FS, see Lilly (2017).
 
    The missing data fraction RR is defined as the ratio of the number of
    missing points in a window of half-width ROUND(L/2) centered on each
    maximum, to the total number of points in the window.  Points in the 
    window but outside the edges of the time series are considered missing.
 
    The missing data fraction can then be used as a constraint to exclude,
    for example, transform maxima with RR > 0.1 or 10% missing data.
    _______________________________________________________________________
 
    See also MAXPROPS, TRANSMAXDIST, ISOMAX, MAX2EDDY.
 
    Usage: [index,ww,ff]=transmax(fs,w);
           [index,ww,ff]=transmax(fs,w,chi);
           [index,ww,ff,rr]=transmax(fs,w,{ga,be,bool});
           [index,ww,ff,rr]=transmax(fs,w,{ga,be,bool},chi);
    _________________________________________________________________
    This is part of JLAB --- type 'help jlab' for more information
    (C) 2017 J.M. Lilly --- type 'help jlab_license' for details        

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