Some extremal properties of Daubechies filters and other orthonormal filters

Authors:
María Elena Domínguez-Jiménez;Paulo J. S. G. Ferreira
Affiliations:
GI TACA, Dept. Matemática Aplicada, ETSII, Universidad Politécnica de Madrid, C/José Gutiérrez Abascal, 2, 28006 Madrid, Spain;Signal Processing Laboratory, IEETA/DETI, Universidade de Aveiro, Portugal
Venue:
Signal Processing
Year:
2011

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Abstract

New extremal properties of Daubechies 4-tap orthonormal filters are given: they maximize a certain functional, have the largest gain in (0,@p/2), and allow maximum energy compaction in [0,@p/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.