# Notes on a New Structure of Active Noise Control Systems
## 1 Introduction  
Active noise control is a very interesting technique used presently by researchers and engineers in different areas of their activity. This technique is applied for attenuation of unwanted waves as well as for the generation of random fields with desired spectral properties [1; 2; 3]. It has a well-established theory that allows one to design hardware and software for adaptive and non-adaptive, single and multi-channel active noise control systems [4; 5; 6; 7; 8]. Active noise control techniques utilize a number of control system structures and control algorithms to attenuate unwanted noise. A feedforward control system structure is applied if measurements of a reference signal giving an additional knowledge about the noise to be attenuated can be obtained. Feedback control system structures are utilized when there are problems with the reference signal acquisition. This implies that values of the reference signal have to be estimated using ideas of the internal model control [6; 9]. Commonly, adaptive control algorithms are applied for the tuning of active noise controllers for two reasons: Initially, to calculate controller coefficients, and next, to update these coefficients to time-varying properties of the noise and the controlled electro-acoustic plant. Adaptation may be performed either in time or in frequency domain basing on the error signal, picked up by the error microphone and then processed by an electronic hardware being the measurement path (an amplifier, antialiasing filter, and A/D converter). Such a processed error signal is used to calculate the coefficients of the active noise controller by minimizing at consecutive discrete-time instants an objective function, that being the corresponding mean square value. For this minimization, an algorithm from a family of least mean square (LMS) algorithms may be applied [10]. It follows from the control theory that each adaptive active noise control system is a nonlinear and time-varying dynamic system, in which the signal at the error microphone and error signal seen by theadaptation algorithm are connected by a nonlinear dynamic relation [11; 12]. Consequently, an adaptation process conducted using the signal obtained at the output of the measurement path may not lead to the greatest possible noise attenuation at the error microphone and the greatest rate of convergence of an adaptation algorithm. To get closer to the optimal solution a modification of an adaptation process is proposed. Its idea is the following: In the adaptation process the input signal of the error signal measurement path is used instead of the corresponding signal output. This input signal is not technically measurable but its values can be estimated using signal processing algorithms. The active noise control algorithm using these signal estimates is considered in the paper. Its origination may be found in a control system structure called the filtered-reference filtered-error LMS (FeFxLMS) algorithm. In this algorithm, an additional discrete-time filter is placed in the error signal measurement path following the A/D converter. This filter may be used for residual error shaping in active noise control [13; 14; 15; 16; 17] or to increase the rate of convergence of the adaptation process [18; 19; 20; 21; 22]. In the paper, a new functionality, not addressed earlier is assigned to this filter. It returns estimates of a signal at the input of the error signal measurement path that are next used in the adaptation process. It is shown in the paper that these estimates influence the behavior of active noise control systems increasing obtained noise attenuation at the error microphone and rate of convergence of active noise control algorithms.