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...
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| Format: | Article |
| Language: | en_US |
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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 |
| _version_ | 1811080480157597696 |
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| author | Demirtas, Sefa Su, Guolong Oppenheim, Alan V. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Demirtas, Sefa Su, Guolong Oppenheim, Alan V. |
| author_sort | Demirtas, Sefa |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:32:21Z |
| format | Article |
| id | mit-1721.1/90496 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:32:21Z |
| publishDate | 2014 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/904962022-10-01T04:16:00Z Sensitivity of polynomial composition and decomposition for signal processing applications Demirtas, Sefa Su, Guolong Oppenheim, Alan V. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Research Laboratory of Electronics Demirtas, Sefa Su, Guolong Oppenheim, Alan V. 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. Texas Instruments Leadership University Consortium Program Bose (Firm) 2014-09-30T19:15:46Z 2014-09-30T19:15:46Z 2012-11 Article http://purl.org/eprint/type/ConferencePaper 978-1-4673-5051-8 978-1-4673-5050-1 978-1-4673-5049-5 1058-6393 http://hdl.handle.net/1721.1/90496 Demirtas, Sefa, Guolong Su, and Alan V. Oppenheim. “Sensitivity of Polynomial Composition and Decomposition for Signal Processing Applications.” 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR) (November 2012). https://orcid.org/0000-0003-0647-236X https://orcid.org/0000-0002-5427-4723 en_US http://dx.doi.org/10.1109/ACSSC.2012.6489032 Proceedings of the 2012 Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR) Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT web domain |
| spellingShingle | Demirtas, Sefa Su, Guolong Oppenheim, Alan V. Sensitivity of polynomial composition and decomposition for signal processing applications |
| title | Sensitivity of polynomial composition and decomposition for signal processing applications |
| title_full | Sensitivity of polynomial composition and decomposition for signal processing applications |
| title_fullStr | Sensitivity of polynomial composition and decomposition for signal processing applications |
| title_full_unstemmed | Sensitivity of polynomial composition and decomposition for signal processing applications |
| title_short | Sensitivity of polynomial composition and decomposition for signal processing applications |
| title_sort | sensitivity of polynomial composition and decomposition for signal processing applications |
| url | http://hdl.handle.net/1721.1/90496 https://orcid.org/0000-0003-0647-236X https://orcid.org/0000-0002-5427-4723 |
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