Inverse kepstrum approach to FIR RLS algorithm and application to adaptive noise cancelling

Abstract

This paper presents inverse kepstrum approach as innovations-based whitening application to FIR RLS filter and its application to two-microphone adaptive noise cancellation. The method uses identification of acoustic path transfer functions between two microphones and the ratio of acoustic path transfer function is then applied as unknown system to adaptive noise cancelling structure. The application is based on innovations-based Wiener filtering structure, where front-end inverse kepstrum (known elsewhere as complex cepstrum) estimates denominator polynomial part with a stable minimum phase from the ratio of overall acoustic transfer function and then a cascaded adaptive zero-model RLS filter estimates remaining part from the overall acoustic transfer function. As a result, it will be shown that an innovations-based kepstrum approach could be applied to adaptive noise cancelling with minimum phase conversion of nonminimum phase term from denominator polynomial, which may naturally be occurred in reverberant room environment, therefore could ultimately give rise to stability of system.