Some properties of the multidimensional complex cepstrum and their relationship to the stability of multidimensional systems
Some properties of the multidimensional complex cepstrum and their relationship to the stability of multidimensional systems
复制标题
多维复倒谱的一些性质及其与多维系统稳定性的关系
DOI：
10.1007/bf01599003
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
D. Goodman
中科院分区：
文献类型：
--
作者：
D. Goodman
得到了在三维晶格上具有任意支撑的anl1序列的倒谱也作为具有任意支撑的anl1序列存在的条件。这些条件用来证明在半空间上有支撑的序列倒谱，当它存在时，在同一半空间上也有支撑。这个结果反过来又用于描述在半空间上具有有界支持的序列倒谱的支持。考虑了倒谱的存在与有界输入、有界输出（BIBO）稳定性之间的关系。最后，计算了逆变算子、同态变换算子及其逆算子的导数。这些结果在一维情况下也很有用。
Conditions are obtained for the cepstrum of anl1 sequence having arbitrary support on theM-dimensional lattice to exist also as anl1 sequence with arbitrary support. These conditions are used to show that the cepstrum of a sequence with support on a half-space will, when it exists, also have support on the same half-space. This result is used, in turn, to describe the support of the cepstrum of a sequence with bounded support on a half-space. The relationship between the existence of the cepstrum and bounded-input, bounded-output (BIBO) stability for all three of these cases is considered. Finally, the derivatives of the inversion operator, the homomorphic transform operator, and its inverse are calculated. These results are also useful in the one-dimensional case.