Stability and Independence for Multivariate Refinable Distributions
Due to their so-called time-frequency localization properties, wavelets have become a powerful tool in signal analysis and image processing. Typical constructions of wavelets depend on the stability of the shifts of an underlying refinable function. In this paper, we derive necessary and sufficient...
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| Veröffentlicht in: | Journal of approximation theory 1999-06, Vol.98 (2), p.248-270 |
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| container_title | Journal of approximation theory |
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| creator | Hogan, Thomas A. |
| description | Due to their so-called time-frequency localization properties, wavelets have become a powerful tool in signal analysis and image processing. Typical constructions of wavelets depend on the stability of the shifts of an underlying refinable function. In this paper, we derive necessary and sufficient conditions for the stability of the shifts of certain compactly supported refinable functions. These conditions are in terms of the zeros of the refinement mask. Our results are actually applicable to more general distributions which are not of function type, if we generalize the notion of stability appropriately. We also provide a similar characterization of the (global) linear independence of the shifts. We present several examples illustrating our results, as well as one example in which known results on box splines are derived using the theorems of this paper. |
| doi_str_mv | 10.1006/jath.1998.3255 |
| format | Article |
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| ispartof | Journal of approximation theory, 1999-06, Vol.98 (2), p.248-270 |
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| language | eng |
| recordid | cdi_crossref_primary_10_1006_jath_1998_3255 |
| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| title | Stability and Independence for Multivariate Refinable Distributions |
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