When the spectrum is simple but poles are very close to the unit circle, then the Toeplitz method may prove more satisfactory. A simple program to do spectral factorization is given in Figure 6 . Insert the additional arrows in Figure 4 which are required when dealing with complex time functions. Show how to do the inverse Hilbert transform, given find u . 3-6 Figure 6 A program to do spectral factorization by means of fast Fourier transform and Hilbert transform.
Complex arithmetic is mandatory.
Results are approximate since integration around the unit circle has been approximated by summation over four points.