A frequency domain implementation of the LMS algorithm has significant advantages. In broadband applications it is important to use the correct window function before Fourier transformation to obtain an unbiased estimation of the required cross correlation function and to eliminate wrap-around effects. In the frequency domain filtered-X LMS algorithm described in this paper, the control filter is updated in the frequency domain as a background task, while control filtering is performed in the time domain, to minimize the processing delays. The frequency domain algorithm showed better performance than the conventional time domain algorithm in simulations of single channel active control systems. The algorithm is also able to improve the convergence of multiple channel systems by compensating for the coupling between the control channels.

Centralized feedforward techniques are often used in active control systems that simultaneously adjust the inputs to multiple secondary sources to minimize the sum of the squared outputs from multiple error sensors. If the number of transducers is large, such centralized control systems require considerable computational power and cabling. In this paper, the stability and performance of decentralized adaptive feedforward systems are considered, in which a number of smaller adaptive controllers are implemented independently, each driving subsets of all the secondary sources to minimize the sum of squared outputs of subsets of the error sensors. The limit of this philosophy is when each secondary source is adjusted to minimize the output of only one error sensor. A general theoretical analysis of such decentralized feedforward controllers is developed. It is also shown that a simple condition can be derived, using the Gerschgorin circle theorem, which provides a sufficient, but not necessary, condition for the stability of the overall system. Unfortunately, this condition appears to be rather conservative for larger systems. Examples of the application of this general analysis are presented for two and three channel active sound control systems operating in free space and a 32-channel sound control system operating in an enclosure. Provided the error sensors are closer to the secondary source used to control them than the other secondary sources, the stability of the control system is seen to be quite robust to decentralization. The steady-state performance is also similar to that of a fully coupled control system, although the transient response generally involves oscillatory modes, which sometimes decay only rather slowly.>