Sensitivity of polynomial composition and decomposition for signal processing applications
Polynomial composition is well studied in mathematics but has only been exploited indirectly and informally in signal processing. Potential future application of polynomial composition for filter implementation and data representation is dependent on its robustness both in forming higher degree poly...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2014
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| Online Access: | http://hdl.handle.net/1721.1/90496 https://orcid.org/0000-0003-0647-236X https://orcid.org/0000-0002-5427-4723 |
| Summary: | Polynomial composition is well studied in mathematics but has only been exploited indirectly and informally in signal processing. Potential future application of polynomial composition for filter implementation and data representation is dependent on its robustness both in forming higher degree polynomials from ones of lower degree and in exactly or approximately decomposing a polynomial into a composed form. This paper addresses robustness in this context, developing sensitivity bounds for both polynomial composition and decomposition and illustrates the sensitivity through simulations. It also demonstrates that sensitivity can be reduced by exploiting composition with first order polynomials and commutative polynomials. |
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