Related properties of minimum-phase and zero-phase time functions
A. J. Berkhout
Journal name: Geophysical Prospecting
Issue: Vol 22, No 4, December 1974 pp. 683 - 709
Info: Article, PDF ( 1.17Mb )
In this paper properties of the discrete zero-phase time function are derived and compared with related properties of the discrete minimum-phase time function.
The two-sided minimum-length signal is introduced and it is derived that, for any given amplitude spectrum, the two-sided minimum-length signal and the signal with zero-phase spectrum are identical signals. A comparison is made between the one-sided minimum-length signal (minimum-phase signal) and the two-sided minimum-length signal (zero-phase signal).
A computational scheme is discussed which determines the zero-phase correspondent of a given signal.
A method is proposed to compute zero-phase least-square inverse filters. The efficiency of minimum-phase and zero-phase least-square inverse filters is shown on signals with different phase properties.
A criterion is derived which determines whether a symmetric time function has the zero-phase property. The close relationship with the minimum-phase criterion is discussed.
Finally the relationship between signal length and resolving power is illustrated on numerical examples.