ELLPARAMS Ellipse parameters of a modulated bivariate or trivariate oscillation. [KAPPA,LAMBDA,THETA,PHI]=ELLPARAMS(X,Y) where X and Y are analytic signals, returns the parameters of the complex-valued signal Z=REAL(X)+i REAL(Y), expressed as a modulated ellipse. Here KAPPA is the RMS ellipse amplitude, LAMBDA is the linearity, THETA is the orientation, and PHI is the instantaneous orbital phase. ELLPARAMS(M), where M is matrix with two columns, also works. See Lilly and Gascard (2006) and Lilly and Olhede (2010a) for details. ELLPARAMS is inverted by ELLSIG, which returns the X and Y signals given the ellipse parameters. ELLPARAMS(...,DIM) performs the analysis with time running along dimension DIM, as opposed to the default behavior of DIM=1. _______________________________________________________________________ Trivariate signals ELLPARAMS also works for trivariate signals, which can be expressed as a modulated ellipse in three dimensions. [KAPPA,LAMBDA,THETA,PHI,ALPHA,BETA]=ELLPARAMS(X,Y,Z), where X, Y, and Z are all analytic signals, also returns the zenith angle ALPHA and the azimuth angle BETA in addition to the other ellipse parameters. ELLPARAMS(M), where M is matrix with three columns, also works. See Lilly (2010) for details on the trivariate case. _______________________________________________________________________ Cell array input / output [KAPPA,LAMBDA,THETA,PHI]=ELLPARAMS(C) also works if C is a cell array containing, say K different X and Y signals, each as a 2-column matrix, C{1}(:,1)=X1, C{1}(:,2)=Y1 C{2}(:,1)=X2, C{2}(:,2)=Y2, ... C{K}(:,1)=XK, C{2}(:,2)=YK. In this case, the output variables will also be length K cell arrays. The trivariate form described above also works, with each cell now being a matrix with three columns. This format works with the cell array output format of RIDGEWALK. __________________________________________________________________ 'ellparams --t' runs a test. See also ELLSIG, ELLBAND, ELLDIFF, ELLVEL, ELLRAD, KL2AB, AB2KL. Usage: [kappa,lambda,theta,phi]=ellparams(x,y); [kappa,lambda,theta,phi]=ellparams(x,y,dim); [kappa,lambda,theta,phi,alpha,beta]=ellparams(x,y,z); [kappa,lambda,theta,phi,alpha,beta]=ellparams([x,y,z]); [kappa,lambda,theta,phi]=ellparams(C); __________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2009--2016 J.M. Lilly --- type 'help jlab_license' for details