圆周卷积算法的改进与实现

Improvement and implementation of circular convolution algorithm

离散卷积是数字信号处理课程中的一种最基本的运算。该算法是在圆周卷积的传统算法上进行研究的,以离散线性卷积和圆周卷积为基本理论基础,引入主值序列矩阵概念。对序列进行补零,将得到的序列依次循环右移,构建主值序列矩阵求解圆周卷积。通过实际算例验证了该算法极大地简化了圆周卷积的运算;在Matlab中,新算法所得的仿真结果与FFT和IFFT实现的仿真结果一致,进一步验证了该方法的有效性和优越性。

The discrete convolution is one of the most basic operation in the course of digital signal processing.The improved algorithm based on the traditional algorithm of circular convolution was a improved research,the paper used the discrete linear convolution and circular convolution as the basic theoretical foundation,introduce the concept of main value sequence marx. Firs4 rotated right the sequence obtained by zero padding in turn to construct the main value sequence matrix,and then to solve the circular convolution.This new algorithm verified by an example,greatly simplifies the circular convolution operation; in Matlab, the simulation results gained by new method are consistent with？the implementation of FFr and IFFT, which further verify the effectiveness and superiority of this method.