Verification of simultaneous equations method by an experimental active noise control system

Abstract

In this study, we verify the performance of the simultaneous equations method using an experimental active noise control system. The simultaneous equations method is based on a priciple different from the filtered-x algorithm requiring a filter modeled on a secondary path from a loudspeaker to an error microphone. Instead of the filter, called the secondary path filter, this method uses an auxiliary filter identifying the overall path consisting of a primary path, a noise control filter and the secondary path. As inferred from the configuration of the overall path, the auxiliary filter can provide two independent equations when two different coefficient vectors are given to the noise control filter. The method thereby estimates the coefficient vector of the noise control filter minimizing the output of the error microphone. In this paper, we propose the application of a frequency domain adaptive algorithm to the identification of the overall path. An improvement in the noise reduction speed is thereby expected. In this paper, we also present computer simulation results demonstrating that the simultaneous equations method can automatically recover the noise reduction effect degraded by path changes, and finally, using an experimental system, we indicate that the method successfully works in practical systems.

Application of simultaneous equations method to sound field creation system

“…In practical use, the loudspeakers are arranged so that the assumption can be satisfied. To derive the optimum inverse filter matrix, the simultaneous equations method [10] first identifies the estimation error between the created sound vector,Ŷ YðzÞ, and the target sound vector, YðzÞ, using the auxiliary filter matrix, SðzÞ. When a tentative inverse filter matrix,Ĥ HðzÞ, is given to the proposed system, the auxiliary filter matrix yields the following relation,…”

“…For applying the above principle to practical systems, the transformation of the transfer function matrix to a filter coefficient matrix is required. In this paper, we apply the frequency domain technique used in [10] to the transformation. In the frequency domain, (16) is rewritten as…”

“…In this paper, we propose to apply the simultaneous equations method [10], proposed for active noise control systems, to the derivation of the inverse filters. The configuration of the active noise control system is almost the same as that of the transaural systems.…”

Verification of extension of simultaneous equations method extended to multiple-channel active noise control systems

“…In practical systems, however, the feeding of the extra noise is undesirable. The simultaneous equations method is well known as a technique capable of automatically recovering the noise reduction effect degraded by the path change without feeding the extra noise [6][7][8]. The method is characterized by an auxiliary filter substituted for the secondary path filter forming the core of the filtered-x algorithm.…”

Active noise control system using IIR lattice filter

“…As a method for perfectly solving this problem, the simultaneous equations method is proposed [6], [7], [8]. This method is characterized by an auxiliary filter substituted for the secondary path filter.…”