Normalized estimate of adaptive filter for non-minimum phase transfer function component: An illustrative case study

This paper presents an analysis of a normalized estimate of an adaptive finite impulse response (FIR) filter for a non-minimum phase transfer function component for the application of a minimum phase kepstrum filter (a ratio of minimum phase filters) to a one-sample delay filter in a beamforming structure. Based on the analysis, it will be shown that a normalized estimate by an adaptive FIR filter is characterized as only one non-minimum phase term from an unknown non-minimum phase system because the adaptive FIR filter estimates a consistent non-minimum phase term in a normalized form from both direct transfer function and its inverted transfer function. Furthermore, it will be shown that the characterized non-minimum phase term from the estimate by the adaptive FIR filter can identify an actual non-minimum phase transfer function component that can be used to evaluate the reverberant level in a realistic environment by monitoring only one zero position from pole-zero placements.