function[signal,a_new,fact]=rescale(signal,a,delta_x1);% This routine calculates the parameters to transform the input for the% fractional Fourier transform when the signal the support of the% input is not N^2 with N=sqrt(length(signal))% Parameters: signal   = the signal to be transformed%             a        = the order of the transform%             delta_x1 = the length of the support of the input signal.% To compute the frft with these data use% Output:     signal = possibly flipped signal to avoid infinite factor%             a_new = compute the frft of order a_new%             fact = and elementwise multiply the result with factN = length(signal);delta_x2 = sqrt(N);k = delta_x2/delta_x1;a_new =  mod(a,4);if k == 1 || a == 0  a_new = a;  fact = 1;  returnelseif a == 2  signal = flipud(signal)else  phi = a*pi/2;  psi = acot(cot(phi)/k^2);  c = csc(phi)/(k*csc(psi));  x = linspace(-delta_x1/2,delta_x1/2,N);  u = x;  nu = c*u;  a_new = 2*psi/pi;  A_phi = exp(-i*(pi*sign(sin(phi))/4-phi/2))/sqrt(abs(sin(phi)));  A_psi = exp(-i*(pi*sign(sin(psi))/4-psi/2))/sqrt(abs(sin(psi)));  fact = A_phi/(k*A_psi)*exp(i*pi*(cot(phi)/c^2-cot(psi))*(nu.^2))';end;