线性卷积与循环卷积等价关系及水声通信应用

Equivalence of Linear Convolution and Circular Convolution and its Application in Underwater Acoustic Communications

线性卷积与循环卷积的等价关系是"数字信号处理"课程的重点内容之一。在计算循环卷积时,通常利用线性卷积的周期延拓来计算周期卷积,再对周期卷积取主值区间得到循环卷积。本文结合水声通信这一海洋信号处理领域的研究热点之一,针对水声通信中最新使用的零填充正交频分复用系统,介绍基于线性卷积的循环卷积计算方法及其具体应用,并通过实例对该方法进行演示。

The equivalence of linear convolution and circular convolution is one of the most important parts in the course of Digital Signal Processing. To compute the circular convolution, we usually use periodic extension of linear convolution to calculate the cyclic convolution, and then extract the principal value interval from the cyclic convolution as the final result of circular convolution. The paper focuses on underwater acoustic communication that is one of the hot topics in oceanic signal processing. In particular, we address zero padding orthogonal frequency division multiplexing （ZP-OFDM） where the computation of the circular convolution based on linear convolution is recently applied. The examples for demonstration are also provided.