function[PH, S]=PhaseTrans1(TH, N); 
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%%%%%%%%%%%%%%%%%%%%%%%%%                      INSERT
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%%      TH:    protophase
%%      N:     order of Fourier terms N. For example N=48.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%            OUTPUT
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%%     PH:    phase
%%     S:     coefficients of the transformation
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S = []; PH = []; % Define Variables

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%%%%%%%%%%%%%%%%%%%%%%                                       COMPUTING TRANSFORMATION COEFFS Sn 
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for n = 1 : (2*N)+1; % Begin of the iteration to compute coefficients S of the transformation
    S(n) = (1 / ( length(TH)*2*pi )) * sum( exp(-i*(n-(N+1))*TH));
end; % End of the iteration
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%%%%%%%%%%%%                                               COMPUTING PHASE FROM COEFFS Sn BY ITERATION OVER N
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PH = TH; % Sn for n = 0
for n = 1 : (2*N)+1;
if (abs((n-(N+1)))>0) PH = PH + 2*pi*S(n) * (exp(i*(n-(N+1))*TH)-1) / (i*(n-(N+1))); end; % Sn for n different from 0
end;
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PH = real(PH); % Eliminating small imaginary parts, which should theoreticall be zero