Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames
We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the original filter bank are preserved. Unitary filter banks providing...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/861563 |
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| author | Martin Ehler |
| author_facet | Martin Ehler |
| author_sort | Martin Ehler |
| collection | DOAJ |
| description | We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the original filter bank are preserved. Unitary filter banks providing perfect reconstruction are induced by tight generalized frames, which enable signal decomposition using a set of linear operators. If, in addition, frame elements have equal norm, then the signal energy is spread through the various filter bank channels in some uniform fashion, which is often more suitable for further signal processing. We start with a given generalized frame whose elements allow for fast matrix vector multiplication, as, for instance, convolution operators, and compute a normalized tight frame, for which signal analysis and synthesis still preserve those fast algorithmic schemes. |
| format | Article |
| id | doaj-art-67365527305548df8ddd3ff36d377a98 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-67365527305548df8ddd3ff36d377a982025-02-03T05:50:42ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/861563861563Preconditioning Filter Bank Decomposition Using Structured Normalized Tight FramesMartin Ehler0Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, AustriaWe turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the original filter bank are preserved. Unitary filter banks providing perfect reconstruction are induced by tight generalized frames, which enable signal decomposition using a set of linear operators. If, in addition, frame elements have equal norm, then the signal energy is spread through the various filter bank channels in some uniform fashion, which is often more suitable for further signal processing. We start with a given generalized frame whose elements allow for fast matrix vector multiplication, as, for instance, convolution operators, and compute a normalized tight frame, for which signal analysis and synthesis still preserve those fast algorithmic schemes.http://dx.doi.org/10.1155/2015/861563 |
| spellingShingle | Martin Ehler Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames Journal of Applied Mathematics |
| title | Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames |
| title_full | Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames |
| title_fullStr | Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames |
| title_full_unstemmed | Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames |
| title_short | Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames |
| title_sort | preconditioning filter bank decomposition using structured normalized tight frames |
| url | http://dx.doi.org/10.1155/2015/861563 |
| work_keys_str_mv | AT martinehler preconditioningfilterbankdecompositionusingstructurednormalizedtightframes |