INSTMOM is the jRidges module of jLab.

 INSTMOM  Univariate and multivariate instantaneous moments.
 
    [A,OMEGA,UPSILON]=INSTMOM(X), where X is an analytic signal, computes 
    the amplitude A, instantaneous *radian* frequency OMEGA, and 
    instantaneous bandwidth assuming a unit sample rate. 
 
    X is an array with the first dimension being "time".  Thus, X can be a 
    matrix of analytic signals oriented as column vectors, or a 2- or 3-D 
    wavelet transform such as output by WAVETRANS.
 
    The output arrays are the same size as X. 
 
    The instantaneous frequency, bandwidth, and curvature are defined as
 
             A    = abs X
           OMEGA  = d/dt Im ln X = d/dt arg X
          UPSILON = d/dt Re ln X = d/dt ln abs X  
   
    where i=SQRT(-1) as usual.
 
    INSTMOM(X,DIM) computes the moments along dimension DIM, instead of 
    the default of computing the moments along the rows (DIM=1).
 
    For details, see 
   
        Lilly & Olhede (2010), "Bivariate instantaneous frequency and 
             bandwidth", IEEE Trans. Sig. Proc., 58 (2), 591--603.
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    Sample interval
 
    INSTMOM(DT,...) uses sample interval DT, where DT is a scalar, for 
    computing time derivatives.  DT=1 is the default.
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    Joint instantaneous moments
 
    INSTMOM can also calculate the joint instananeous moments of 
    multivariate signals, as defined in Lilly and Olhede (2010).
 
    [JA,JOMEGA,JUPSILON]=INSTMOM(X1,X2,...,XN,DIM) returns the *joint*
    instantaneous moments calculated across the N signals X1,X2,... XN, 
    based on the univariate instantaneous moments along dimension DIM.
 
    The joint instantaneous amplitude JA is the root-mean-square of the 
    component amplitudes across dimension JDIM, while JOMEGA is power-
    weighted average of the component instantaneous frequencies.
 
    For details and for the definition of the joint instantaneous bandwidth 
    JUPSILON, see Lilly and Olhede (2010).
 
    [JA,JOMEGA,JUPSILON]=INSTMOM(X,DIM,JDIM) also works, where the joint
    instantaneous moments are calculated across dimensions JDIM of X.
 
    The joint instantaneous moments JA, JOMEGA, and JUPSILON then have the 
    same size as X, except along dimension JDIM where they have only one 
    entry.  Note that DIM is no longer optional when JDIM is used.
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    Instantaneous curvature
 
    INSTMOM can also return the next-higher order instantaneous moment, 
    which is more rarely encountered. 
 
    [A,OMEGA,UPSILON,XI]=INSTMOM(X) returns the instantaneous curvature XI,
    defined as
 
             XI   = d^2/dt^2 abs X / abs X + i d^2/dt^2 arg X
                  = UPSILON^2 + d/dt UPSILON + i d/dt OMEGA
 
    Similarly [JA,JOMEGA,JUPSILON,JXI]=INSTMOM(X,DIM,JDIM) returns the
    joint instantaneous curvature JXI for the multivariate signal X.
     
    For details on the univariate and joint instantaneous curvature, see 
 
        Lilly and Olhede (2012a), "Analysis of modulated multivariate 
             oscillations", IEEE Trans. Sig. Proc., 60 (2), 600--612. 
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    Boundary conditions
 
    The first and last points must be treated differently, as the central 
    difference is not defined there.  Three different methods can be used.
 
    INSTMOM(...,STR) specifies the method: STR= 'endpoint' (the default),
    'periodic', or 'nans'.  See VDIFF for details.   
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    'instmom --f' generates some sample figures.
 
    Usage: [a,om]=instmom(x);
           [a,om,up,xi]=instmom(dt,x);
           [a,om,up,xi]=instmom(dt,x,dim);
           [a,om,up,xi]=instmom(dt,x1,x2,x3,x4,dim);
           [a,om,up,xi]=instmom(dt,x,dim,jdim);
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    This is part of JLAB --- type 'help jlab' for more information
    (C) 2007--2015 J.M. Lilly --- type 'help jlab_license' for details

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