Adaptive Fractional Fourier Domain Filtering in Active Noise Control

Abstract

Acoustic noise control systems gain more importance as more and more industrial equipments, i.e., engines, fans, ventilators, and exhausters are in use (1–6). Passive acoustic noise control techniques benefit enclosures, barriers and silencers to attenuate ambient noise. However, if the noise has dominant low-frequency components, then passive techniques are either inefficient or expensive. In contrast, active noise control (ANC) systems are much more effective in canceling low-frequency noise. Various noise cancelation algorithms have been proposed in the literature (7–11). In a generic ANC scheme, a reference microphone is used to receive the ambient noise and the system produces an anti-noise signal which has equal amplitude but opposite phase with the primary noise to cancel it acoustically (1). As the primary noise may have time-varying characteristics, ANC systems should be able to adapt themselves to the noise rapidly. In most of the ANC systems, either adaptive filters or neural network based structures are employed (2–6; 9; 12–18). In (15), fuzzy-neural networks are used to estimate the nonlinear response of the unknown primary acoustic path where primary and secondary paths are characterized by nonlinear functions. On the other hand adaptive filters are usually employed to increase the system performance and robustness. They are mostly employed with least mean squares (LMS)-based algorithms and the adaptation is usually realized in time domain (3; 9; 12; 13; 19). Whereas Fourier domain (20) and wavelet-based adaptive filter bank approaches (21; 22) are among the few transform-domain adaptation techniques that have been used in the ANC systems. Compared to time-domain adaptive filters, transform-domain adaptive filters may need fewer parameters (23; 24). When the noise source has dominant low-frequency components, wavelet transform-based adaptive filters provide higher performance rates. However, in case of linear frequency modulated (LFM) or chirp-type audio signals, as their frequency varies linearly with time, performance rates are limited for both Fourier and wavelet-transform domains. LFM signals are among the frequently used signals in real life and they are good models for mechanical systems with accelerating internal components. A Gaussian enveloped,