phaseran.m

混沌动力学实例仿真

function s=phaseran(x,c)
%Syntax: s=phaseran(x,c)
%_______________________
%
% Makes c phase randomized surrogates of a time series x.
%
% s is the phase randomized time series.
% x is the original time series.
% c is the number of surrogates.
%
%
% References:
%
% Theiler J, Galdrikian B, Longtin A, Eubank S, Farmer D J (1992): Using 
% Surrogate Data to Detect Nonlinearity in Time Series. In Nonlinear Modeling
% and Forecasting, eds. Casdagli M & Eubank S. 163-188. Addison-Wesley
%
% Theiler J, Eubank S,Galdrikian B, Longtin A,  Farmer D J (1992): Testing
% for nonlinearity in time series: the method of surrogate data. Physica D
% 58: 77-94
%
% 
% Alexandros Leontitsis
% Department of Education
% University of Ioannina
% 45110 - Dourouti
% Ioannina
% Greece
%
% University e-mail: [e-mail]
% Lifetime e-mail: [e-mail]
% Homepage: http://www.geocities.com/CapeCanaveral/Lab/1421
%
% 12 Apr 2002

if nargin<1 | isempty(x)==1
   error('You should provide a time series.');
else
   % x must be a vector
   if min(size(x))>1
      error('Invalid time series.');
   end
   x=x(:);
   % N is the time series length
   N=length(x);
end

if nargin<2 | isempty(c)==1
   c=1;
else
   % c must be scalar
   if sum(size(c))>2
      error('c must be scalar.');
   end
   % c must be greater or equal than 1
   if c<1
      error('c must be greater or equal than 1.');
   end
end


% FFT on x
y=fft(x);
% Magnitudes
m=abs(y);
% Angles
p=angle(y);
% The imaginary unit
i=sqrt(-1);
% Half of the data points
h=floor(N/2);

for j=1:c
   % Randomized phases
   if rem(N,2)==0
      p1=rand(h-1,1)*2*pi;
      p(2:N)=[p1' p(h+1) -flipud(p1)'];
      % Adjust the magnitudes
      m=[m(1:h+1);flipud(m(2:h))];
   else
      p1=rand(h,1)*2*pi;
      p(2:N)=[p1 -flipud(p1)];
   end
   % Back to the complex numbers
   s(:,j)=m.*exp(i*p);
   % Back to the time series (phase randomized surrogates)
   s(:,j)=real(ifft(s(:,j)));
end