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

<div class="WordSection1"><p class="MsoNormal">&nbsp;</p></div><p><span style="font-size: 10.0pt; font-family: 'Times New Roman',serif; mso-fareast-font-family: SimSun; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;"><br style="page-break-before: always; mso-break-type: section-break;" clear="all" /> </span></p><p class="Abstract" style="text-indent: 13.6pt;"><em>Abstract</em>—In the field of digital filters, 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 have a high demand for hardware resources, many researchers have explored the use of recursion to reduce the use of adders in circuits to reduce the hardware cost of digital filters. Among them, the RAG-N algorithm and the BHM algorithm are some of the better-known algorithms in this field. This study focuses on the quantization performance of finite impulse response filter coefficients and coefficient optimization via recursive algorithms. We have designed and demonstrated the structure of a finite impulse response filter optimized using the recursive algorithm after 8-bit, 10-bit, and 12-bit quantization, and built the corresponding simulation models using Simulink. Our results show that while heuristic optimization algorithms such as RAG-N and BHM can significantly reduce the use of hardware resources, the computation time of these algorithms may increase as the number of quantization bits increases and may have an impact on the circuit design due to the increase in logic depth and the increase in path delay. Therefore, future research needs to pay further attention to these issues to improve the performance and efficiency of FIR filters.</p>