Estimating Transformation Length in Linear- to Minimum-Phase Transformation Using Cepstrums

A systematic procedure for estimation of the transformation length in linear- to minimum-phase FIR-filter transformation using complex cepstrums is presented in this paper. The basis of the method is an introduced disturbing function. This function describes how aliasing affects the final frequency response of the minimum-phase FIR-filter.

The transformation length estimation is made using the absolute value of the dominating zero in the linear-phase FIR-filter and the maximum allowed amplitude and phase deviation of the disturbing function. Two examples are given. The first one verifies the introduction of the disturbing function while the second example uses the proposed procedure to estimate the necessary transformation length for a linear-phase lowpass filter.