On a generalized factorization problem for structurally passive synthesis of digital filters
TL;DR: It is shown that, in one dimension, a discrete domain algorithm for synthesizing previously unpublished internally passive structures and alternative methods of synthesis for more conventional structures such as the cascade structure can always be performed.
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Abstract: The problem of structurally passive synthesis of multidimensional digital filters of the quarter-plane causal type as an interconnection of more elementary building blocks directly in the discrete domain is addressed by means of the factorization of the chain matrix, the hybrid matrix and the transfer function matrix associated with a prescribed multidimensional lossless two-port By using recent results on the discrete domain representation of such matrices, a generalized lossless two-port matrix is introduced to present all three factorizations in a unified setting Necessary and sufficient conditions for factorability as well as an algorithm for computing these factors when they exist are obtained In particular, it is shown that, in one dimension the factorizations can always be performed Thus, in one dimension, a discrete domain algorithm for synthesizing previously unpublished internally passive structures and alternative methods of synthesis for more conventional structures such as the cascade structure are also obtained >
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Citations
Notes on \sl n -D Polynomial Matrix Factorizations
TL;DR: A relationship between the prime factorizability of a normal full rank n-D ( n>2) polynomial matrix and its reduced minors is discussed and a partial solution to one of the conjectures is provided.
A generalization of Serre's conjecture and some related issues
Zhiping Lin,Nirmal K. Bose +1 more
TL;DR: The generalized Serre conjecture is proved to be equivalent to several other unsettled conjectures and, therfore, all these conjectures constitute a complete set in the sense that solution to any one also solves all the remaining as discussed by the authors.
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•Posted Content
A Generalization of Serre's Conjecture and Some Related Issues
Zhiping Lin,Nirmal K. Bose +1 more
TL;DR: The generalized Serre conjecture is proved to be equivalent to several other unsettled conjectures and, therfore, all these conjectures constitute a complete set in the sense that solution to any one also solves all the remaining as discussed by the authors.
46
Factorizations for nD polynomial matrices
TL;DR: In this article, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a given nD (n > 2) polynomial matrix whose maximal order minors satisfy certain conditions.
Structural passive synthesis of three-dimensional recursive cone filters
TL;DR: In this article, a simple analytical design method for structurally passive three-dimensional recursive cone filters is presented, where the cone filter is realized by cascading two structural passive 2D recursive fan filters having different passband orientations, and the orientation of the passband is easily obtained by choosing the proper orientations of the two two-dimensional fan filters.
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References
Wave digital filters: Theory and practice
Alfred Fettweis
- 01 Feb 1986
TL;DR: Wave digital filters (WDFs) as discussed by the authors are modeled after classical filters, preferably in lattice or ladder configurations or generalizations thereof, and have very good properties concerning coefficient accuracy requirements, dynamic range, and especially all aspects of stability under finite-arithmetic conditions.
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