Iterative techniques for minimum phase signal reconstruction from phase or magnitude

In this report, we develop iterative algorithms for reconstructing a minimum phase sequence from the phase or magnitude of its Fourier transform. The iterative techniques result in two potentially important computational algorithms. The first is a means of implementing the Hilbert transform of the log-magnitude or phase of the Fourier transform of a minimum phase sequence. This procedure avoids problems of phase unwrapping and aliasing inherent in the direct discrete Fourier transform implementation of the Hilbert transform. The second algorithm is a new method of computing samples of the unwrapped phase. As compared with other available phase unwrapping algorithms, this approach does not rely on adding 2 pi multiples to samples of the principal value of the phase.