Adaptive Signal Processing Systems for Active Control of Acoustic Noise on Circular Paths Iman Tabatabaei Ardekani † and Waleed Abdulla* *Unitec Institute of Technology, New Zealand † The University of Auckland, New Zealand Keywords: Active noise control, adaptive signal processing, acoustic noise. Abstract Adaptive active noise control (ANC) systems create a silent point at the location of an error microphone. This silent point can creates a surrounding zone of quiet with small dimensions. Moreover, the error microphone has to be located within the zone of quiet, limiting the effective space available in the zone of quiet. This paper develops a new adaptive signal processing system for ANC in a circular path, centred at the error microphone. It is shown that an optimal controller for the creation of a silent point on a circular path around the error microphone can be constructed by the series combination of a digital controller, called the circular controller, and a Wiener-Hopf filter. The transfer function of the circular controller is derived based on the system model in the acoustic domain. An update equation for the automatic adjustment of the Wiener-Hopf filter in the proposed system is developed. The proposed system is verified by using different computer simulations. 1 Introduction Active noise control (ANC) is widely used in the control of low frequency acoustic noise. Several electronic control architecture for ANC systems have been proposed so far, including analogue feedback, model-based and adaptive digital filtering (ADF) architectures [1]. Among them, ADF architecture shows a high level of reliability and efficiency. In this architecture, an adaptive algorithm is responsible for updating the control system parameters in accordance with the statistics of the noise level at the desired silent point. Because of this updating system, ANC systems with this architecture are usually classified as adaptive ANC [2]. Filtered x Least Mean Square (FxLMS) algorithm is one of the most popular adaptive algorithms that can be used in adaptive ANC applications [3]. In the past few years, we have studied the behaviours of the FxLMS algorithm and determined the shortcoming of FxLMS-based adaptive ANC systems [4-6]. One of which is that they are only able to create a silent point at the location of an error microphone. Moving towards surpassing this problem is the main motivation of this paper. In adaptive ANC, a digital filter drives a secondary source in such a way that the noise level at the location of an error microphone becomes minimal [4]. The sound field generated by this source (secondary or control field) is superposed to the primary sound field (or noise field). FxLMS can adaptively update the control system parameters in such a way that the superposition of the two fields is minimized at the location of the error microphone. In this situation, a silent point is created at the error microphone location and, consequently, a zone of quiet is produced around this point as a by-product [7]. A single silent point in a pure-tone diffuse sound field establishes a spherical zone of quiet with at least 10 dB of noise reduction within its volume [7]. This zone is centred at the silent point and its radius is 1/20 of the noise wavelength. Hence, single-channel ANC systems are only able to make small zones of quiet. Moreover, the error microphone has to be located at the centre of the quiet zone, resulting in a very small space for even a human ear to be located in the zone of quiet. For solving this problem, a multichannel structure can be used to create several (discrete) silent points [8]. Consequently, the created silent points can make a larger zone of quiet. This improvement can be achieved only at the cost of using more hardware. By applying virtual acoustic sensing techniques, one can remove the error microphone from the zone of quiet [9]. This system can be potentially used for applications like ANC-based hearing aids, where locating an error microphone within the zone of quiet (eardrum) is technically impossible. As an additional advantage, the effective space within the zone of quiet is extended because there is no error microphone in the zone. This paper develops a novel adaptive signal processing system for making silence on a spatial circular path around the error microphone. The core of this method is a virtual acoustic sensing mechanism that is able to estimate the spatial distribution of the acoustic pressure on a circular path centred at the error microphone location. An adaptive signal processing algorithm is then developed to estimate the control system parameters in such a way that the noise level in the circular path becomes minimal. It is still required to place an error microphone at the centre of the circular path in order to measure a feedback signal from the zone of quiet. 2 Modelling ANC in acoustic domain Fig. 1 shows a typical block diagram for single-channel FxLMS-based adaptive ANC [4]. In this figure, G and H represent the primary and secondary paths respectively. The reference signal, x(n), is measured by a microphone located close to the noise source. The error signal, e(n), is measured by the error microphone, located at the desired silent point. The digital controller, W is a finite impulse response (FIR) filter that generates the control signal, y(n), to drive the control source. ISBN: 978-0-9891305-3-0 ©2013 SDIWC 69