# Dynamic Matching of Reconstruction and Anti-Aliasing Filters in Adaptive Active Noise Control
## 1 Introduction  
Noise control methods can be divided into two main categories: passive noise control and active noise control (ANC) [1]. Passive noise control methods can be used to effectively suppress middle- and high-frequency noise but hardly reduce low-frequency noise. Meanwhile, ANC technology offers an effective means of low-frequency noise control, and has been widely applied in active headphones and headrests, as well as in noise reduction for ventilation ducts [2]. The application of ANC technology in headphones is the most mature; however, wearing headphones may introduce ear-blocking effects, making users feel uncomfortable and causing interference in their actions or communications [3]. Hence, the local active noise control technology represented by active noise reduction headrests is flourishing. It has also found applications in scenarios such as automotive road noise control and aircraft cabin noise control, and related research is constantly being deepened [4; 5; 6; 7]. Active noise control can be conducted with fixed coefficient methods and adaptive methods [1; 8]. Fixed coefficient methods typically used in ANC headphones have a simple calculation process; thus, they can be applied for real-time control at high sampling rates [9; 10]. Adaptive methods have significant advantages in tracking changes in the sound field environment, and are widely used in active headrests; however, their computational complexity may be much higher. Improving the sampling rate of a system helps to accelerate its response speed, but this poses significant challenges related to the real-timecomputing performance and data throughput of the processor [10; 11]. Therefore, researching methods for improving the noise reduction ability without increasing the requirements of computational performance is important. At the algorithmic level, the FxLMS and NFxLMS algorithms are the two most basic types of algorithms used in the field of adaptive active noise control [12]. In addition, modified methods such as frequency-domain adaptive algorithms, multi-subband filtering algorithms, and delay-free subband filtering algorithms have emerged one after another [11; 13]. As the partitioned block frequency-domain method uses different filter lengths to control noise at different frequencies, the computational requirements are further deducted in the low-frequency control process of these optimization algorithms [14]. These optimization algorithms successfully accelerate the convergence speed of ANC systems, improve their robustness, and reduce their computational requirements. As the research deepens, the impact of the group delay introduced by hardware systems and algorithms in the control process has received much attention. [PERSON] et al. first emphasized the importance of causal constraints on the active control of sound [15]. [PERSON] et al. conducted an in-depth analysis of the group delay effect [1] and further studied the frequency-domain adaptation of causal digital filters [16]. With the increase in local active noise control systems in practical application scenarios, more discussions about group delay and causality have been conducted [17; 18; 19]. In order to avoid the limitations imposed by the spatial distance on the group delay, [PERSON] et al. proposed an increase in the distance between the reference microphone and the error microphone using wireless transmission [20]. However, this method does not allow for long-frame caching and has extremely demanding delay requirements for the wireless transmission system. At the system level, the aliasing noise, mirror noise, and group delay introduced by control circuits have gradually received attention [21; 22; 23]. The aliasing noise represents the noise in the low-frequency band introduced by the high-frequency component in the extraction process, and the mirror noise represents the high-frequency noise correlated with the low-frequency signal in the interpolation or reconstruction process. To reduce the electronic delay of a single-rate ANC system, [PERSON] et al.