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