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Dominguez-Jimenez-2011a

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Article

Title Some extremal properties of Daubechies filters and other orthonormal filters
Author M. Elena Domínguez-Jiménez, Paulo J S G Ferreira
Journal Signal Processing
Volume 91
Number 1
Pages 85-89
Month January
Year 2011
DOI 10.1016/j.sigpro.2010.06.011
Group
Group (before 2015) Signal Processing Laboratory
Indexed by ISI Yes

Abstract

New extremal properties of Daubechies 4-tap orthonormal filters are given: they maximize a certain functional, have the largest gain in (0,π / 2), and allow maximum energy compaction in [0,π / 2]. These properties do not carry over to Daubechies filters of arbitrary length. They complement what is known about Daubechies filters and highlight the specific role of the 4-tap filter. Moreover, we demonstrate that these properties cannot be fulfilled by any other orthonormal lowpass filter, regardless of its length.