Related Properties of Minimum‐phase and Zero‐phase Time Functions *

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.