用快速哈达玛变换(FHT)实现高速线性卷积  

Implement high speed linear convolution using fast hadamard transform

作　　者：乔志伟[1] 魏学业[1] 韩焱[1] 

机构地区：[1]北京交通大学电子信息工程学院,北京100044

出　　处：《电子测量与仪器学报》2010年第3期263-267,共5页Journal of Electronic Measurement and Instrumentation

基　　金：国家自然科学基金项目(编号:60772102;60602041;60532080)资助项目;山西省自然科学基金项目(编号:2007012003)资助项目;电子测试技术国防科技重点实验室基金项目(编号:9140C1204040908)资助项目;山西省高校科技项目(编号:20091020)资助项目

摘　　要：为了加速实现长序列的线性卷积,提出了用快速哈达玛变换(FHT)实现线性卷积的快速算法。分析了哈达玛变换的特点和快速算法的时间复杂度,设计了用FHT计算线性卷积的矩阵表达式,并推导出了哈达玛域滤波器的增益矩阵的求解公式,分析了该方法的加速原理及其适用条件。理论分析和实验表明,该方法比FFT线性卷积法快了近一倍。To speedup the convolution process of long sequence signals,a fast linear convolution algorithm using fast Hadamard transform was proposed.The characteristics of Hadamard transform and its time complexity were analyzed.The matrix expression of using FHT to calculate linear convolution was designed.The equation of the Hadamard filter gain matrix was deduced.The acceleration principle and applicable condition of the method were analyzed.Theoretical analysis and experiment demonstrate that the method is faster than the FFT-convolution method for about one time.

关 键 词：线性卷积 圆周卷积 加速 哈达玛变换 沃尔什变换 

分 类 号：TN911.72[电子电信—通信与信息系统]