卷积移位性质的研究

Research on the Shift Property of Convolution

卷积是一种重要的积分变换方法,在现代信号处理技术的多个领域都有非常广泛的应用,许多有待深入研究的新课题也有赖于卷积。卷积本身蕴含着某些特殊的性质,这些性质不仅能够简化卷积的运算过程,而且能够揭示卷积运算的内在规律。移位运算是一种非常重要的信号运算,广泛存在于信号处理过程中,通过对卷积的定义和已有性质的进一步研究,结合卷积定理和傅里叶变换理论,提出并证明了卷积的移位性质及其推论。

Convolution is an important integral transformation method,which has a very wide applications in many fields of modern signal processing technology.Many new topics to be further studied also depend on convolution integral.The convolution integral itself contains some special properties,which can not only simplify the convolution operation,but also reveal the inner principle of the convolution operation.Shift operation is a very important signal operation method,which is widely used in signal processing.Through the research of convolution definition and existing properties,combined with convolution theorem and Fourier transform theory,the shift property of convolution integral and its inference are proved.