Minimum-phase signal calculation using the real cepstrum

Adrian D. Smith and Robert J. Ferguson

ABSTRACT

The concept of minimum phase in geophysics is an important one, especially for processes such as statistical deconvolution which assume the condition in the source wavelet. We wish to have an alternative method to the Hilbert transform to convert a signal of arbitrary phase to its minimum-phase equivalent, while retaining the same amplitude spectrum. We implement a minimum-phase reconstruction based on the real cepstrum developed for finite-impulse response (FIR) filters by treating the signal as a filter. We demonstrate that the algorithm is able to handle signals with ill-conditioned amplitude spectra and still give minimum-phase outputs through analysis of pole-zero plots, along with a simple deconvolution test. We also introduce two metrics: the Pole-Zero Ratio (PZR) and Pole-Zero Distance (PZD) as potential quantitative descriptions of how close a signal is to being minimum phase.

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