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- Title
Tensor z-Transform.
- Authors
Chang, Shih Yu; Wu, Hsiao-Chun
- 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.
- Subjects
CAUCHY integrals; MIMO systems; SYSTEM analysis; IMPULSE response; PSYCHOLOGICAL feedback
- Publication
Journal of Applied Mathematics, 2024, Vol 2024, p1
- ISSN
1110-757X
- Publication type
Article
- DOI
10.1155/2024/6614609