Phase Estimation of Minimum Phase Systems using the Hartley Phase Cepstrum

E. Chilton and E. Hassanain (UK)


Hartley transform, phase modelling, cepstrum analysis. In section 2 of this paper, the Hartley phase spectrum and the Hartley phase cepstrum are defined and their application to phase analysis is explained. In section 3, examples are presented of the phase modeling for various system input signals. A method for the removal of phase discontinuities is described and a method for selecting the system phase response from the Hartley phase cepstrum is discussed. In section 4 the conclusions a


this problem [5] [6] but having done so, the phase spectrum still contains other discontinuities which originate from the signal itself. For successful modeling of the system phase response, these latter discontinuities, which are assumed to be introduced by the input signal to the system, must also be removed. The assumption here is that the system being modeled is a minimum phase system. In this paper the Hartley Transform is presented as a novel alternative to the conventional Fourier Transform, for the estimation of the phase response of linear discrete minimum phase systems. The representation of phase via the Hartley transform avoids the need for a phase unwrapping algorithm and the Hartley phase spectrum has the added advantage of being a function bounded by ±√2. An algorithm for removing other discontinuities arising from the signal itself in the Hartley phase spectrum is introduced. The Hartley phase cepstrum is defined and a technique for system phase estimation is discussed and illustrated with suitable examples. In this paper, we present a novel approach to the problem of modeling the phase response via the Hartley transform (H.T). The representation of phase from the H.T circumvents the use of an inverse trigonometrical function and, thus, obviates the need for phase unwrapping. However, other discontinuities are present which need to be removed from the Hartley phase spectrum. This paper restricts discussion to the one-dimensional case of phase analysis of the output of a minimum phase system. However, potentially, it could be extended to the two-dimensional case with imaging applications.

Important Links:

Go Back