Following the comment by David Goodmanson above, here is what I used to randomize an array of timeseries data:
function randX = phaseRandomize(X)
% Returns a phase-randomized version of the input data X. If X is an array,
% each row is treated as an independant time series, and columns represent
% sample points.
[N,L]=size(X);
Y=fft(X,[],2); % Get spectrum
% Add random phase shifts (negative for conjugates), preserve DC offset
rnd_theta= -pi + (2*pi).*rand(N,L/2-1);
Y(:,2:L/2)=Y(:,2:L/2).*exp(1i*rnd_theta);
Y(:,L/2+2:L)=Y(:,L/2+2:L).*exp(-1i*flip(rnd_theta,2));
% return phase-randomized data
randX =ifft(Y,[],2);
end
