| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1709581 | Applied Mathematics Letters | 2008 | 6 Pages |
Abstract
The precise Sobolev exponent s∞(φn)s∞(φn) of the Butterworth refinable function φnφn associated with the Butterworth filter of order nn, bn(ξ)≔cos2n(ξ/2)cos2n(ξ/2)+sin2n(ξ/2), is shown to be s∞(φn)=nlog23+log2(1+3−n)s∞(φn)=nlog23+log2(1+3−n). This recovers the previously given asymptotic estimate of s∞(φn)s∞(φn) of Fan and Sun, and gives more accurate regularity of Butterworth refinable function φnφn.
Related Topics
Physical Sciences and Engineering
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Computational Mechanics
Authors
Hong Oh Kim, Rae Young Kim,