The efficacy of active noise control technology in mitigating urban noise, particularly in relation to low-frequency components, has been well-established. In the realm of traditional academic research, adaptive algorithms, such as the filtered reference least mean square method, are extensively employed to achieve real-time noise reduction in many applications. Nevertheless, the utilization of this technology in commercial goods is often hindered by its significant computing complexity and inherent instability. In this particular scenario, the adoption of the fixed-filter strategy emerges as a viable alternative for addressing these challenges, albeit with a potential trade-off in terms of noise reduction efficacy. This work aims to conduct a theoretical investigation into the synchronization error of the digital Active Noise Control (ANC) system. Keywords: Fixed-filter, Active noise control, Multichannel active noise control.

翻译：主动噪声控制技术在缓解城市噪声，特别是低频噪声成分方面的有效性已得到充分证实。在传统学术研究领域，自适应算法（如滤波参考最小均方法）被广泛应用于众多场景，以实现实时降噪。然而，该技术在商业产品中的应用常常因其较高的计算复杂度和固有的不稳定性而受到限制。在此特定情况下，采用固定滤波器策略成为解决这些挑战的可行替代方案，尽管可能在降噪效果上有所折中。本文旨在对数字主动噪声控制系统的同步误差进行理论研究。关键词：固定滤波器，主动噪声控制，多通道主动噪声控制。