## 5 Conclusions  
Through the analysis of the WSMANC algorithm, the time-domain adaptive filter coefficient update process and the convolution calculation process of obtaining the time-domain filter reference signal led to an increase in the calculation of the WSMANC algorithm in the form of a power function. Aiming at decreasing the WSMANC algorithm's calculation, the SFDFBANC algorithm is proposed in the paper. The algorithm uses total acoustic delay as the estimated secondary path information, which can avoid the computational complexity of obtaining the secondary path information process by using the offline modeling or online modeling methods. It also implements the adaptive filter coefficient update process in the frequency domain and replaces the convolution computational complexity with the frequency-domain multiple to produce the filtered internal synthesis signal. As such, the computational complexity changes in the form of a logarithmic function by increasing the number \(N\) of the adaptive filter length, which reduces the calculation complexity. Compared to both the WSMANC and SAIMC algorithms, if only the variable \(N\) is not less than 64, the SFDFBANC algorithm has the least calculation complexity. The primary sound sources were single-frequency noise, narrowband white noise, and narrowband pink noise to verify the characters of the SFDFBANC algorithm. The proposed SFDFBANC algorithm has the fastest convergence rate, and the effect of noise reduction is equivalent to that of the WSMANC algorithm and the SAIMC algorithm after reaching the steady state.  
In this paper, the signal frequency and narrowband noise signals were adopted as the noise sources. In forthcoming research, the main areas of study are as follows:  
1. The proposed algorithm will adopt the subband adaptive filter method to expand the primary noise frequency range. The proposed algorithm will be investigated for its potential application in broadband active noise control.
2. Study the stability of the feedback ANC algorithm. There is a closed loop in the feedback ANC system, so the poles always exist in the system function. When the frequency of primary noise is located on the pole, the ANC system will be unstable. In the following study, we will research the adaptive method to obtain the frequency information of the pole, which can improve the stability of feedback ANC algorithm and help the proposed SFDFBANC algorithm in broadband active noise control applications.  
Figure 19: Computational complexity.  
**Author Contributions:** Conceptualization, Y.G., M.G. and G.Y.; methodology, M.G. and G.Y.; software, Y.G. and M.G.; validation, Y.G., M.G. and G.Y.; formal analysis, Y.G. and M.G.; investigation, Y.G., M.G. and G.Y.; resources, G.Y.; data curation, Y.G., M.G. and G.Y.; writing--original draft preparation, Y.G. and M.G.; writing--review and editing, G.Y.; visualization, Y.G. and G.Y.; supervision, G.Y.; project administration, Y.G.; funding acquisition, M.G. All authors have read and agreed to the published version of the manuscript.  
This work was jointly supported by the National Natural Science Foundation of China under Grant (No. 51902300) and the Natural Science Foundation of Zhejiang Province under Grant (No. LQ19A040003).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.