Some extremal properties of Daubechies filters and other orthonormal filters |
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| Authors: | Marí a Elena Domí nguez-Jimé nez,Paulo J.S.G. Ferreira |
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| Affiliation: | a GI TACA, Dept. Matemática Aplicada, ETSII, Universidad Politécnica de Madrid, C/José Gutiérrez Abascal, 2, 28006 Madrid, Spain
b Signal Processing Laboratory, IEETA/DETI, Universidade de Aveiro, Portugal |
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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,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. |
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| Keywords: | Daubechies filters Energy compaction Extremal properties Filter banks |
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