二维Z变换中的时域卷积定理探讨

On Theorem of 2-D Time-domain Convolution in 2-D Z-transfotm

该文给出了二维时域卷积定理的完整描述，包括二维单边、双边时域序列及二维单边、双边Ｚ变换的不同组合情形下，时域卷积定理的描述及定理的证明。由于卷积在数学定义上的特殊性，导致卷积序列在二、三、四象限的值对结果的第一象限值有影响，而单边Ｚ变换仅对序列第一条限值进行计算，两者在定义上的差异及统一正是该文所研究的问题。

This paper gives a complete description of 2-D time-domain convolution the-orem,including the rigid proof of different combinations of 2.D two-sided and/or one-sided time sequences and 2-D one-sided and/or two-sided Z-transform. Because of specialdefinition of convolution in mathematics,the convolution results in quadrant 1 one influ-enced by the value of sequence in quadrant 2、3、4. But one-sided Z-transform is onlybased on the sequences in quadrant 1.The difference and unity between both above arewhat this paper discusses.