New Coefficient Update Method for Feedback Control Filters in Active Noise Control System

A feedforward active noise control system includes the secondary path filter for compensation of acoustic coupling between loudspeaker and reference microphone. In ordinary systems, the filter is designed to be a pre-set type, without any system identification for it, because the adaptation of its filter taps without any additional noise is difficult. This paper introduces a new identification method for the secondary path filter. It forms two independent equations by using the estimation error resulted by the two sets of different coefficients of the noise control filter. A numerical method is also described as a practical technique to solve the equations. 1 INTRODUCTION The feedforward type of active noise control system consists of three filters, the noise control filter, secondary path filter and the feedback control filter [1]. The adaptive filtering technique is applied only to the noise control filter in ordinary systems. The coefficients of the other filters are fixed to the values estimated by extra noise signal fed previously to starting the noise control. However, the continuous refreshment of these two filters are also necessary to avoid instability of the system and considerable worst case where the system falls into uncontrollable [2]. The conventional way of refreshing the coefficients of these filters, feeding the extra noise to the secondary source [3], makes a problem. The authors already presented a method to refresh the coefficients of the secondary path filter without feeding any extra noise [4] This paper proposes a new refreshment way named ”simultaneous equations method” for the coefficients of the feedback control filter without feeding any extra noise. 2 PRINCIPLE The available signal for identification calculation is only the output of the noise detection microphone, while this output involves two unknowns related to the feedback path and the primary source. The method given here composes two equations relating to the two different estimation errors involved in the noise control filter coefficients at the different point of time, and applies the linear prediction analysis to the signal in order to form two equations. The linear prediction filter coefficients consequently yield two equations corresponding to the noise control filter coefficients with different estimation errors. These simultaneous equations are solvable, and one of the solutions gives the impulse response of the feedback path. The feedback path from the secondary source to the noise detection sensor forms the closed loop shown in Fig. 1. For this loop, the input signal of the noise control filter is expressed as Copyright SFA InterNoise 2000 2 Figure 1: Feedback loop structured by the feedback path. X (z) = W (z) 1 + H (z) { B (z)− B̂ (z) } (1) by using H (z ), B(z ) , B̂ (z) and W (z ) which are the transfer functions of the noise control filter, feedback path, feedback control filter and the primary noise, respectively. We see only X (z ) is available for updating the coefficients of the feedback control filter. This input signal, however, has two unknowns, namely, B(z ) and W (z ). Here, we suppose that the primary noise is synthesized through the following process by dividing U (z ), the linearly unpredicted and P(z ) the linearly predicted components: W (z) = U (z) 1− P (z) , P (z) = K ∑