摘要
利用线性卷积计算循环卷积是信息处理的一种重要手段。在时域分析中,指出了利用线性卷积计算循环卷积的关键技术是在信号左端补元素,使系统函数与信号相对应,给出了信号补元素的3种方法:顺取法、反转法与倍补法,推导了线性卷积计算循环卷积的公式。在频域分析中,指出了循环卷积变换到频域的条件是系统函数与信号长度相等,且信号要延拓为周期信号。分析了信号周期延拓与系统函数右端补0元素的方法,推导了由傅里叶变换的性质计算循环卷积的方法。给出了循环卷积的时域与频域算法流程图。
Circular convolution calculation using the linear convolution is an important means of informanon processing, In the time domain analysis, the key technology to calculate circular convolution using the linear convolution, which is to add signal elements to the left of the signal, so that the system function elements can he corresponded by the signal elements, is discussed. Three ways to get signal elements from the signal, those are in the index ascending order, in the index descending order, and many times of the signal are given, formula of circular convolution calculation using linear convolution are derived. In the frequency domain analysis, the conditions to transform the circular convolution to the frequency domain are pointed, those are the system function and the signal has the same length, and the signal has to be period. The method of the signal periodic extension and adding zeros to the right of the system function is analyzed, and the circular convolution algorithm by Fourier transform is derived. Circular convolution algorithm flowcharts in the time domain and frequency domain are presented.
出处
《计算机工程与设计》
CSCD
北大核心
2014年第5期1678-1682,共5页
Computer Engineering and Design
基金
国家创新方法工作专项基金项目(2012IM010200)
