Recursive Algorithm FIR Filter Quantization and Low-Cost Structure Optimization Design Based on MATLAB and Simulink

In the field of digital filtering, finite impulse response (FIR) filters are favored for their stable structure and linear phase characteristics. However, since conventional direct-type filters are slow in operation and require significant hardware resources, many researchers have explored the use of recursive methods to reduce the use of adders in circuits, thereby reducing the hardware cost of digital filters. Among them, the RAG-N algorithm and the BHM algorithm are among the more well-known algorithms in the field. The focus of this study is on the quantization performance of the coefficients of finite impulse response filters and the analysis of coefficient optimization by recursive algorithms. In this paper, the structure of finite impulse response filter optimized by recursive algorithm after 8-bit, 10-bit and 12-bit quantization is firstly designed and demonstrated, and the corresponding simulation model is constructed by using Simulink on this basis. The final results show that although heuristic optimization algorithms like RAG-N and BHM can significantly reduce the use of hardware resources, the computational time of these algorithms may increase as the number of quantization bits increases, which may have an impact on the circuit design due to the increase in the logic depth and the increase in the path delay. Therefore, future research should pay more attention to these issues to improve the performance and efficiency of FIR filters.