面向嵌入式系统的有效值快速算法  

Fast Algorithm of RMS Oriented to Embedded Systems

作　　者：马文博 罗丹 蒋玉华 张亿宗 廖志贤[1] 黄国现[1] MA Wenbo;LUO Dan;JIANG Yuhua;ZHANG Yizong;LIAO Zhixian;HUANG Guoxian(School of Electronic and Information Engineering/School of Integrated Circuits,Guangxi Normal University,Guilin 541004,China;Institute of Technology,Guilin University,Guilin 541006,China)

机构地区：[1]广西师范大学电子与信息工程学院/集成电路学院,广西桂林541004 [2]桂林学院理工学院,广西桂林541006

出　　处：《计算机测量与控制》2023年第6期204-211,共8页Computer Measurement &Control

基　　金：2022年度广西高校中青年教师科研基础能力提升项目(2022KY1574);国家级大学生创新创业训练计划项目(202210602080)。

摘　　要：ADC采样交流波形是嵌入式系统的一项重要应用,当采集到的电压波形并非标准函数波形(如正弦波、三角波等)的畸变波形时,不能直接通过简化数学公式或平均响应法求得其均方根值;为得到任意波形的均方根值,首先需要求出该波形的频率(或周期);在传统算法中,需要进行FFT(快速傅里叶变换),该算法需要大量内存空间和较高时间复杂度,且只能进行2N个点运算,精度和分辨率受限;因单片机片上资源有限,该算法并不适合多路实时运算;为改进以上不足,设计了一种峰值(谷值)查找算法,该算法拥有O(n)时间复杂度,实时性好;通过该算法寻找采样波形中三个峰值点,确定波形的其中一个周期,进而计算得到均方根值;相比FFT算法,该算法运行速度提升93倍,空间复杂度降低为FFT的1/300,且在实际应用中运行稳定可靠,平均误差低于0.6%。The alternating current(AC)waveform of analog to digital(ADC)sampling is an important application of embedded systems.When a collected voltage waveform is not a standard function waveform(such as sine wave,triangle wave,etc.),the root mean square(RMS)of waveform cannot be directly calculated by a simplified mathematical formula or average response method.In order to get the RMS value of any waveform,the frequency(or period)of waveform is firstly calculated;In traditional algorithms,RMS value needs to be performed by fast Fourier transform(FFT),which requires a large number of memory space and high time,and the accuracy and resolution of waveform are limited by the calculation of only 2N points;Due to the limited resources of single-chip microcomputer,the algorithm is not suitable for multi-channel and real-time calculation;A peak(valley)searching algorithm is proposed to improve above deficiencies,the algorithm has the time complexity of O(N)and good real-time performance;The algorithm is used to find three peak points in the sampled waveform,determine one of the cycles of the waveform,and then calculate the RMS value;Compared with the FFT algorithm,the running speed of this algorithm is increased by 93 times,the space complexity is reduced to 1/300,with an average error of less than 0.6%,the proposed algorithm runs stably and reliably,and it can be further promoted and used in practical applications.

关 键 词：嵌入式 STM32 峰值查找 有效值 任意波形 

分 类 号：TP311.1[自动化与计算机技术—计算机软件与理论]