ELLSIG Creates a modulated elliptical signal in two or three dimensions. Z=ELLSIG(KAPPA,LAMBDA,THETA,PHI) creates a time-varying, complex-valued elliptical signal Z=X+iY characterized by RMS amplitude KAPPA, linearity LAMBDA, orientation THETA, and orbital phase PHI. [X,Y]=ELLSIG(KAPPA,LAMBDA,THETA,PHI) returns the analytic part of the ellipse signal along the X and Y axes. See Lilly and Gascard (2006) and Lilly and Olhede (2010a) for details. ELLSIG is inverted by ELLPARAMS, which returns the ellipse parameters given the analytic signals X and Y. ______________________________________________________________________ Three dimensions ELLSIG can also generate an elliptical signal in three dimenions. [X,Y,Z]=ELLSIG(KAPPA,LAMBDA,THETA,PHI,ALPHA,BETA) returns the analytic part of the ellipse signal along the X, Y, and Z axes. Here BETA is the "zenith angle" giving the orientation of the plane containing the ellipse with respect to the vertical, while ALPHA is the "azimuth angle", the angle the normal to the plane of the ellipse makes with the x-axis. In the trivariate case, LAMBDA is positive, and the direction of rotation of the particle projected onto the X-Y plane is changed by letting the zenith angle BETA exceed PI/2. See Lilly (2011) for details on the trivariate case. __________________________________________________________________ Cell array input / output ELLSIG also works if the input arguments are cell arrays of numeric arrays, in which case the output arguments will also be cell arrays of the same size. ______________________________________________________________________ [X,Y]=ELLSIG(...,'real') or [X,Y,Z]=ELLSIG(...,'real') takes the real part of the output arguments. ______________________________________________________________________ 'ellsig --t' runs some tests. Usage: z=ellsig(kappa,lambda,theta,phi); [x,y]=ellsig(kappa,lambda,theta,phi); [x,y,z]=ellsig(kappa,lambda,theta,phi,alpha,beta); __________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2007--2013 J.M. Lilly --- type 'help jlab_license' for details