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Theory Of Regular MBand Wavelet Bases
 IEEE TRANS. ON SIGNAL PROCESSING
, 1993
"... This paper constructs Kregular Mband orthonormal wavelet bases. Kregularity of the wavelet basis is known to be useful in numerical analysis applications and in image coding using wavelet techniques. Several characterizations of Kregularity and their importance are described. An explicit formula ..."
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Cited by 78 (6 self)
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This paper constructs Kregular Mband orthonormal wavelet bases. Kregularity of the wavelet basis is known to be useful in numerical analysis applications and in image coding using wavelet techniques. Several characterizations of Kregularity and their importance are described. An explicit formula is obtained for all minimal length Mband scaling filters. A new statespace approach to constructing the wavelet filters from the scaling filters is also described. When Mband wavelets are constructed from unitary filter banks they give rise to wavelet tight frames in general (not orthonormal bases). Conditions on the scaling filter so that the wavelet bases obtained from it is orthonormal is also described.
Optimal wavelet representation of signals and wavelet sampling theorem
 IEEE Trans. Circuits Syst. II
, 1994
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Wavelets And Filter Banks
 IN WAVELETS: A TUTORIAL IN THEORY AND APPLICATIONS
, 1991
"... Wavelet and shorttime Fourier analysis is introduced in the context of frequency decompositions. Wavelet type frequency decompositions are associated with filter banks, and using this fact, filter bank theory is used to construct multiplicity M wavelet frames and tight frames. The way in which filt ..."
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Cited by 8 (6 self)
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Wavelet and shorttime Fourier analysis is introduced in the context of frequency decompositions. Wavelet type frequency decompositions are associated with filter banks, and using this fact, filter bank theory is used to construct multiplicity M wavelet frames and tight frames. The way in which filter banks lead to decomposition and recomposition of arbitrary separable Hilbert spaces is also described. Efficient computational structures for both filter banks and wavelets are also discussed.
On The Moments Of The Scaling Function
, 1992
"... This paper derives relationships between the moments of the scaling function /0(t) associated with multiplicity M , Kregular, compactly supported, orthonormal wavelet bases [6, 5], that are extensions of the multiplicity 2, Kregular orthonormal wavelet bases constructed by Daubechies [2]. One suc ..."
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Cited by 5 (1 self)
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This paper derives relationships between the moments of the scaling function /0(t) associated with multiplicity M , Kregular, compactly supported, orthonormal wavelet bases [6, 5], that are extensions of the multiplicity 2, Kregular orthonormal wavelet bases constructed by Daubechies [2]. One such relationship is that the square of the first moment of the scaling function (/0(t)) is equal to its second moment. This relationship is used to show that uniform sample values of a function provides a third order approximation of its scaling function expansion coefficients. For the special case of M = 2, the results in this paper have been reported earlier [3]. 1. INTRODUCTION In this paper we derive relationships between the moments of the scaling function /0(t) associated with the compactly supported, multiplicity M , K regular, orthonormal wavelet bases. In particular, we show that the square of the first moment of /0 is the second moment of /0 . Hence samples of a function accurately ...