An adaptive IIR digital filter based on estimation of the allpass system and minimum-phase system

This paper presents the IIR adaptive digital filter. The maximum-phase shift component of the unknown system is estimated by an allpass adaptive digital filter. The impulse response of the residual part of the system is concentrated in the neighborhood of time n = 0 and is then estimated by a transversal adaptive digital filter. As a first step, the transfer function of the unknown system is represented by an orthogonal function that contains an allpass function and has poles only at the origin of the z-plane. Then, an IIR adaptive digital filter with the same structure as that of the unknown system is considered, and its derivation algorithm is presented. The convergence value of the tap coefficient for a white input signal is derived based on the orthogonality principle and the properties of the minimum-phase system. The following properties are shown. When the order of the allpass function is the same as that of the unknown system, the tap coefficients of any allpass part converge to the tap coefficients of the allpass part of the unknown system. When the order of the adaptive digital filter is less than that of the unknown system, the tap coefficients converge to some of the tap coefficients of the unknown system. The latter result is important from a practical viewpoint. It is also shown that the tap coefficients of the minimum-phase part satisfy the condition for the Wiener solution. Lastly, the convergence behavior and the convergence value are examined by simulation. ©1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(4): 79–88, 1999