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Tensor z-Transform.
- Source :
- Journal of Applied Mathematics; 4/8/2024, Vol. 2024, p1-21, 21p
- Publication Year :
- 2024
-
Abstract
- The multi-input multioutput (MIMO) systems involving multirelational signals generated from distributed sources have been emerging as the most generalized model in practice. The existing work for characterizing such a MIMO system is to build a corresponding transform tensor, each of whose entries turns out to be the individual z -transform of a discrete-time impulse response sequence. However, when a MIMO system has a global feedback mechanism, which also involves multirelational signals, the aforementioned individual z -transforms of the overall transfer tensor are quite difficult to formulate. Therefore, a new mathematical framework to govern both feedforward and feedback MIMO systems is in crucial demand. In this work, we define the tensor z -transform to characterize a MIMO system involving multirelational signals as a whole rather than the individual entries separately, which is a novel concept for system analysis. To do so, we extend Cauchy's integral formula and Cauchy's residue theorem from scalars to arbitrary-dimensional tensors, and then, to apply these new mathematical tools, we establish to undertake the inverse tensor z -transform and approximate the corresponding discrete-time tensor sequences. Our proposed new tensor z -transform in this work can be applied to design digital tensor filters including infinite-impulse-response (IIR) tensor filters (involving global feedback mechanisms) and finite-impulse-response (FIR) tensor filters. Finally, numerical evaluations are presented to demonstrate certain interesting phenomena of the new tensor z -transform. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1110757X
- Volume :
- 2024
- Database :
- Complementary Index
- Journal :
- Journal of Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176503866
- Full Text :
- https://doi.org/10.1155/2024/6614609