## 1 Introduction  
The basic idea of active noise control (ANC), first conceptualized by [PERSON] in his US patent [1], is very simple: two out of phase acoustic waves would result in a destructive interference and hence cancel each other out. Therefore, any ANC system would essentially generate an anti-phase (acoustic) noise-cancelling signal, which is combined acoustically with the primary (disturbance or noise) signal generated from some noise source (for example, exhaust fan, vacuum cleaner, power transformer, etc.). These two signals, being anti-phase to each other, tend to cancel each other out [2]. Active noise and vibration control is a well-researched area that has spread from academic research in a tight laboratory settings to successful commercial products, thanks to great advancements in the modern semiconductor technology. Many successful applications of ANC technology have been reported in [3; 4; 5; 6; 7; 8] (among others); however, the most popular is ANC headsets [9; 10]. An excellent survey on recent research trends and interesting applications for ANC systems can be found in [11; 12]. Broadly speaking, the ANC systems can be classified as single-channel ANC or multi-channel ANC, depending upon the number of sensors and actuators deployed to cover the area of interest. Here, only single-channel ANC has been considered, and the presented methods can be fairly easily extended for the multichannel ANC if needed. Furthermore, we consider acoustic noise sources without loss of generality, as the presented methods can be modified for application to active vibration control. In a basic setting of a single-channel scenario, the ANC system generally comprises one primary/reference sensor (e.g., microphone), one secondary actuator (e.g., loudspeaker), and one error sensor (e.g., microphone). The objective of the reference microphone is to pick-up the reference/input noise prior to it propagating via the primary path and appearing around the error microphone--the location where the noise reduction is desired. An adaptive control filter generates the secondary (cancelling) signal, which is propagated via the secondary path between the loudspeaker and the error microphone. The ANC adaptive filter is adapted in such a way that the secondary (cancelling) signal is anti-phase to the primary noise appearing around the error microphone. This results in a destructive interference around the error microphone; hence, the error microphone records the residual noise, which, in turn, is used to guide adaptation of the control filter. Due to the presence of a secondary (electro-acoustic) path between the cancelling loudspeaker and the error microphone, the classical least mean square (LMS) algorithm [13; 14] cannot be directly implemented. In a variant of the LMS algorithm, the effect of the secondary path is compensated by employing a secondary path model to filter the reference signal and then use this filtered-reference signal in the LMS update equation, resulting in the so-called filtered-reference LMS, most commonly abbreviated as filtered-x (Fx) LMS (FxLMS) algorithm [3]. The classical FxLMS algorithm has been a first choice for practical ANC systems, mainly due to its reduced computational cost and simple implementation. However, the classical FxLMS algorithm suffers from slow convergence speed and shows poor performance (being a stochastic gradient-based algorithm) for non-Gaussian sources. In order to address slow convergence speed, different ANC algorithms have been proposed with improved convergence properties, viz., (1) lattice-ANC systems [15]; (2) infinite impulse response (IIR) filter-based LMS algorithms called Filtered-u Recursive LMS (FuRLMS) [16], and filtered-v algorithms [17]; (3) recursive least squares (RLS)-based algorithms called FxRLS [3] and Fx Fast-Transversal-Filter (FxFTF) [18]; and (4) frequency-domain-ANC systems (see [19] and references therein).