重叠保留法教学探索与案例设计  

作　　者：黄荣宗 蓝丽娟 陈志文[2] 蒋朝辉[2] 许可 

机构地区：[1]中南大学能源科学与工程学院,长沙410083 [2]中南大学自动化学院,长沙410083 [3]国防科技大学电子科学学院,长沙410073

出　　处：《高教学刊》2024年第12期130-133,共4页Journal of Higher Education

基　　金：2023年国家自然科学基金面上项目“微尺度功能表面上气液相变的介微观建模与直接模拟研究”(52376086);2021国家自然科学基金青年项目“非一致标准具效应下微量气体原位检测方法研究”(62103448);2022年湖南省科技创新计划项目“青年科技人才项目”(2022RC1090)。

摘　　要：分段卷积是DFT/FFT实现线性卷积的重要途径,主要有重叠保留法和重叠相加法,教学过程中发现,学生对于重叠保留法的学习往往忽略对算法原理的真正理解,导致计算结果不准确。该文基于圆周卷积与线性卷积的数学关系,推导重叠保留法计算误差出现的原因,得到重叠保留法的计算步骤;结合计算流程和具体实例,分析造成计算数据缺失的原因,并创新提出解决方法;随后分析基2-FFT算法下补零处理对重叠保留法的影响,得出采用重叠保留法和FFT算法计算线性卷积的优化步骤;最后,以调制光谱分析为例进行教学案例设计,并对重叠保留法给出相应的教学建议。Piecewise convolution is an important way for DFT/FFT algorithm to calculate linear convolution.It mainly includes overlapping reservation and overlap-add methods.During the teaching process,students often ignore the principle of the algorithm when learning the overlapping reservation method,resulting in calculation errors.Based on the mathematical relationship between circular convolution and linear convolution,this article deduces the reasons for the calculation error of the overlapping reservation method,and obtains the calculation process of the overlapping reservation method.Combining the calculation process and specific examples,it analyzes the reasons for the missing calculation data,and innovatively proposes the solution.Then,it analyzes the impact of zero-padding processing on the overlapping preservation method under the base 2-FFT algorithm,and optimizes the steps for calculating linear convolution using the overlapping reservation and FFT algorithms.Finally,a teaching case is designed using the modulation spectrum analysis,and corresponding teaching suggestions are given for the overlapping reservation method.

关 键 词：分段卷积 重叠保留法 线性卷积 圆周卷积 案例设计 

分 类 号：G642[文化科学—高等教育学]