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