## 1 Introduction  
In recent years, advanced adaptive algorithms have attracted much interest in the development of effective active noise control (ANC) systems [1; 2]. Specifically, the affine projection (AP) algorithm [3] has emerged as an attractive solution for effective noise reduction since this algorithm converges more rapidly than the least mean square (LMS) algorithm; however, their high computational cost restricts its use in some ANC applications. Currently, new alternatives to reduce the computational cost of the AP algorithms have been proposed. As a consequence, these new approaches potentially allow the construction of efficient ANC systems [4; 5]. For example, [PERSON] et al. [6] proposed a new variant of filtered-x AP (FXAP) algorithm, which is based on an affine projection-like (APL-I) algorithm, to significantly minimize the computational cost and maintain the high convergence speed compared with that of the conventional FXAP algorithms. In fact, their proposed algorithm can thus be potentially used in ANC systems that require lower computational power compared to AP algorithms and to retain a high convergence speed when compared with existing approaches. Even with these advantages, system performance can be improved because the algorithms based on affine projections suffer from a large steady-state mean square error (MSE) [6; 7; 8], causing less noise reduction. To improve the MSE, variable-step algorithms have been presented [4]. Nevertheless, the user must know some parameters a priori, which are not always available, to ensure the proper operation of the algorithm. Recently, alternative methods based on combination schemes to ensure high convergence speed and small MSE have been reported [9; 10; 11]. These combination schemes are commonly composed of a fast filter and a slow filter. The use of a fast filter results in a rapid convergence rate, while a slow filter yields a steady-state MSE. With respect to this application, very few works have been proposed to process ANC systems using convex combination methods. In particular, [PERSON] et al. [12] presented an alternative method based on convex combination of filtered-x least mean square (FXLMS) algorithms for single-channel and multichannel ANC systems. However, the convergence speed is slow, and the overall computational cost is very high since both adaptive filters operate simultaneously during the entire process. [PERSON] et al. [13] proposed a convex combination based on a functional link artificial neural network (FLANN) filter along with a Volterra filter for a single-channel ANC system. Their proposal focused on nonlinear adaptive filters. Additionally, both filters process the signals concurrently, similar to in the previous case [12]. Recently, [PERSON] et al. [14] developed a convex combination of the filtered-X least mean fourth (FXLMF) and FXLMS algorithms. However, both algorithms belong to the LMS family, resulting in a slow convergence speed. Recently, [PERSON] et al. [15] proposed a combination of two filtered-x generalized mixed norm (FXGMN) algorithms for a single-channel ANC system. This algorithm exhibits lower computational cost than AP algorithms, because this approach is based on LMS algorithms. However, the user must adjust several parameters to tune the algorithm by trial and error, resulting a significant time-consuming. Analyzing previous works, these approaches employ at least twice the computational burden when compared with conventional adaptive filters. Therefore, the development of alternative methods with low computational complexity, low MSE and high convergence speed to efficiently process multichannel ANC systems is still a great challenge. In this paper, we present a scheme based on the filtered-x affine projection-like (FXAPL-I) and FXLMS algorithms for single-channel and multichannel ANC applications. In our scheme, high convergence speed with a lower MSE is achieved by alternating the selection between these filters. Therefore, it is not necessary to enable both filters during the entire process.