On vector Karhunen-Loeve transforms and optimal vector transforms
作者： Xiang-Gen Xia , B.W. Suter
DOI: 10.1109/76.465094
关键词:
摘要: We first prove that the vector Karhunen-Loeve (VKL) transform for any finite many vector-valued signal, x/sub 1/,/spl middot//spl middot/,x/sub L/, exists. The VKL is equivalent to scalar KL scalar-valued signal X=(x/sub 1//sup T/,/spl L//sup T/)/sup T/. Based on transforms, we provide a necessary and sufficient condition existence of optimal transforms (unitary). With condition, one can see unitary do not exist in most cases, therefore needs use suboptimal transforms. then nonunitary L/ exists when all eigenvalues correlation matrix X are nonzero. formulate via >
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