Active noise control algorithms that use the adaptive signal processing technology have been widely investigated and applied in practical situations after Filtered-X LMS algorithm had been proposed by Widrow [1]. The development of Filtered-U LMS algorithm by Eriksson [2] enabled us to control lightly damped systems with long impulse responses or a system with acoustic feedback paths, with a much smaller number of "lter weights.
Adaptive FIR or IIR "lter structures are usually used for ANC algorithms to reduce undesired noise in time-varying environment. In practical applications, the FIR "lter is the most popular because of its stability and linear characteristics. However, adaptive algorithms with FIR structures need a large number of weights to control the lightly damped systems. They try to minimize the error with equal weights for all the frequency components if the reference signal is white noise unless the band pass "lters are applied to reference and error signals. In many practical ANC systems, where the reference or desired error signals are narrow band, it is ine$cient to control such a system with an FIR "lter because we cannot select the control frequency range where the control e!orts should be concentrated on.
In this study, a new adaptive "lter structure is proposed for ANC systems with banded noise. Constructing an adaptive "lter with a linear combination of stable IIR "lter bases, we can save much computational power without instability and non-linearity problems, which are usually associated with the conventional IIR adaptive "lters. Also, we can selectively choose the control frequencies by appropriately setting the IIR bases. One possible choice for each IIR base is an exponentially enveloped sinusoidal function. The proposed IIR-based adaptive "lter needs a smaller number of adaptive weights than the FIR "lter for lightly damped systems or narrow banded noise control.
In section 2, an IIR-based "lter is proposed and Filtered-X LMS algorithm using the IIR-based "lter is derived. Selection of IIR "lter bases is discussed in section 3 and three methods to improve the computational e$ciency are proposed in section 4. Results of the simulation and the experiment in section 5 demonstrate the feasibility of the proposed algorithm. Conclusions are drawn in section 6.