📄 adjph.m
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function ox=adjph(x)%ADJPH Normalization of columns of a complex matrix.%% Given a complex matrix X, OX=ADJPH(X) returns the complex matrix OX% that is obtained from X by multiplying column vectors of X with% phase factors exp(i*phi) such that the real part and the imaginary% part of each column vector of OX are orthogonal and the norm of the% real part is greater than or equal to the norm of the imaginary% part.%% ADJPH is called by ARMODE.%% See also ARMODE.% Modified 16-Dec-99% Author: Tapio Schneider% tapio@gps.caltech.edu for j = 1:size(x,2) a = real(x(:,j)); % real part of jth column of x b = imag(x(:,j)); % imag part of jth column of x phi = .5*atan( 2*sum(a.*b)/(b'*b-a'*a) ); bnorm = norm(sin(phi).*a+cos(phi).*b); % norm of new imaginary part anorm = norm(cos(phi).*a-sin(phi).*b); % norm of new real part if bnorm > anorm if phi < 0 phi = phi-pi/2; else phi = phi+pi/2; end end ox(:,j) = x(:,j).*exp(i*phi); end
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