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Signal Processing 86 (2006) 16321647 Tight and sibling frames originated from discrete splines$

Summary: Signal Processing 86 (2006) 1632≠1647
Tight and sibling frames originated from discrete splines$
Amir Z. Averbuch√, Valery A. Zheludev, Tamir Cohen
School of Computer Science, Tel Aviv University, 69978 Tel Aviv, Israel
Received 19 August 2004; received in revised form 27 May 2005
Available online 12 October 2005
We present a new family of frames, which are generated by perfect reconstruction filter banks. The filter banks are based
on the discrete interpolatory splines and are related to Butterworth filters. Each filter bank comprises one interpolatory
symmetric low-pass filter, one band-pass and one high-pass filters. In the sibling frames case, all the filters are linear phase
and generate symmetric scaling functions with analysis and synthesis pairs of framelets. In the tight frame case, all the
analysis waveforms coincide with their synthesis counterparts. In the sibling frame, we can vary the framelets making them
different for synthesis and analysis cases. This enables us to swap vanishing moments between the synthesis and the
analysis framelets or to add smoothness to the synthesis framelets. We construct dual pairs of frames, where all the
waveforms are symmetric and the framelets may have any number of vanishing moments. Although most of the designed
filters are IIR, they allow fast implementation via recursive procedures. The waveforms are well localized in time domain
despite their infinite support.
r 2005 Elsevier B.V. All rights reserved.
Keywords: Frame; Filter bank; Discrete spline
1. Introduction


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences