ELLBAND is the jEllipse module of jLab.

 ELLBAND  Bandwidth of modulated elliptical signals in two or three dimensions.
 
    [A,B,C]=ELLBAND(KAPPA,LAMBDA,THETA,PHI) computes the instantaneous 
    bandwidth of the elliptical signal characterized by RMS amplitude 
    KAPPA, linearity LAMBDA, orientation THETA, and orbital phase PHI.
 
    The three output arguments are
 
           A  - Amplitude modulation bandwidth  
           B  - Deformation bandwidth
           C  - Precession bandwidth. 
 
    and these satisfy UPSILON^2=A^2+B^2+C^2 where UPSILON is the joint 
    instantaneous bandwidth of the bivariate signal.
 
    The form of these terms is as follows:
 
          A = 1/KAPPA d/dt KAPPA 
          B = 1/2 * 1/SQRT(1-LAMBDA^2) *  d/dt LAMBDA 
          C = LAMBDA d/dt THETA
 
    [A,B,C,UPSILON]=ELLBAND(KAPPA,LAMBDA,THETA,PHI) also returns the total 
    instantaneous bandwith UPSILON=SQRT(A^2+B^2+C^2).
 
    ELLBAND(...,DIM) performs the analysis with time running along
    dimension DIM, as opposed to the default behavior of DIM=1.
 
    For details see Lilly and Olhede (2010).
 
    ELLBAND also works if the input arguments are cell arrays of numerical
    arrays, in which case the output will be similarly sized cell arrays.
    __________________________________________________________________
 
    Three dimensions
 
    ELLBAND can also compute the instantaneous bandwidth of modulated 
    elliptical signals in three dimensions.
 
    [A,B,C,D,E]=ELLBAND(KAPPA,LAMBDA,THETA,PHI,ALPHA,BETA) returns the
    terms in the bandwidth from a modulated ellipical signal in a plane
    with a normal vector having azimuth angle ALPHA and zenith angle BETA.
    
    The five output arguments are
 
           A   - Amplitude modulation bandwidth, as in 2D 
           B   - Deformation bandwidth, as in 2D
           C   - Precession bandwidth, as in 2D
           D   - Precession bandwidth with full 3D effects
           E   - Bandwidth due to motion of the normal to the plane
 
    and these, in principle, satisfy UPSILON^2=A^2+B^2+C^2+D^2+|E|^2 where 
    UPSILON is the joint instantaneous bandwidth of the trivariate signal.
    See below for a caveat on this statement.
 
    Terms A--C are just as in the bivariate case.  The new terms are:
 
          D = LAMBDA [d/dt THETA + COS(BETA) * d/dt ALPHA]
          E = N^T X_+ / |X_+^H X_+|    
    
    where N is the trivariate normal vector, X_+ is the trivariate analytic
    signal vector, and "T" denotes the matrix transpose, and "H" the 
    Hermitian transpose.  Note that term E may be complex-valued.
 
    Note that term C does not contribute to the full bandwidth, but is 
    output in order to compare the two-dimensional and three-dimensional
    effects in the full precession bandwidth, term D.
 
    An important point is that the trivariate ellipse parameters can be 
    ill-defined for a nearly linear signal, and the elliptical bandwidth 
    terms can give erroneously large values at isolated points.  To check
    for this, compare with the joint bandwidth from INSTMOM.
 
    [A,B,C,D,E,UPSILON]=ELLBAND(KAPPA,LAMBDA,THETA,PHI,ALPHA,BETA) also 
    returns the total bandwith UPSILON=SQRT(A^2+B^2+C^2+D^2+|E|^2).
 
    For details see Lilly (2011).
    __________________________________________________________________
 
    ELLBAND(DT,...) sets the sample interval DT, which defaults to DT=1.
    DT may be a scalar, or if the input fields are cell arrays having
    length N, DT may be a numerical array of length N. 
    
    See also ANATRANS, WAVETRANS, INSTMOM.
 
    'ellband --t' runs a test.
    'ellband --f' generates a figure from Lilly and Olhede (2010).
 
    Usage:  [a,b,c]=ellband(kappa,lambda,theta,phi);
            [a,b,c]=ellband(dt,kappa,lambda,theta,phi);  
            [a,b,c]=ellband(dt,kappa,lambda,theta,phi,dim);  
            [a,b,c,upsilon]=ellband(dt,kappa,lambda,theta,phi,dim);  
            [a,b,c,d,e]=ellband(kappa,lambda,theta,phi,alpha,beta); 
            [a,b,c,d,e]=ellband(dt,kappa,lambda,theta,phi,alpha,beta);    
    __________________________________________________________________
    This is part of JLAB --- type 'help jlab' for more information
    (C) 2006--2014 J.M. Lilly --- type 'help jlab_license' for details

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