W. M. Lawton. Necessary and Sufficient Conditions for Existence of Orthornomal Wavelet Bases. Journal of Math. Physics, 1990. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Wavelets And Filter Banks - Gopinath, Burrus (1991) (Correct)
....little do with the fact that there exist scaling functions and wavelets. In summary, given a unitary filter bank with a DC condition, there exist wavelet tight frames. In the multiplicity M case also necessary and sufficient conditions for orthonormality of the bases can be worked out as in [28, 20]. An important point to note is that most of the tight frames would be orthonormal bases. Once we have an orthonormal basis, we can impose regularity on the functions i(t) or equivalently on 0(t) Most of the work in [7] is in constructing wavelets with arbitrary large degree of ....
W. M. Lawton. Necessary And Sufficient Conditions for Existence Of on Wavelet Bases. Journal of Math. Physics, 1990.
Time Localization Techniques for Wavelet Transforms - Mladen Victor Wickerhauser (1994) (1 citation) (Correct)
.... quadrature filter sequences fg(k)g and fg 0 (k)g via the formulas below, using any integer M : g(k) Gamma1) k h 0 (2M 1 Gamma k) g 0 (k) Gamma1) k h(2M 1 Gamma k) 21) We also have the following result, which is related to Lemma 12 in [6] and a similar result in [11]: Lemma 2.8 The biorthogonal QF conditions imply H 1 = H 0 1 = 1 p 2 1. Proof: With exact reconstruction, 1 = Gamma H 0 H G 0 G Delta 1 = p 2 H 0 1, since H1 = p 2 1 and G1 = 0. Likewise, 1 = H H 0 G G 0 ) 1 = p 2 H 1, since H 0 1 = p 2 1 and ....
Wayne M. Lawton. Necessary and sufficient conditions for existence of orthonormal wavelet bases. Journal of Mathematical Physics, 32:57--61, 1991.
Theory Of Regular M-Band Wavelet Bases - Steffen, Heller, Gopinath, Burrus (1993) (11 citations) (Correct)
....of Erlangen Nurnberg, Germany y Aware Inc. Cambridge, MA z Rice University, Houston, TX x Rice University, Houston TX 1 Introduction In recent years wavelet orthonormal bases have been constructed and studied extensively from both a mathematical and a signal processing point of view [6, 27, 28, 5, 3, 47, 48, 36]. One reason that wavelets are interesting is that they overcome some of the shortcomings of short time Fourier decompositions [30, 17, 48, 7, 20, 13] by decomposing a signal into channels that have the same bandwidth on a logarithmic scale. Thus high frequency channels have wide bandwidth and ....
....general give rise only to wavelet tight frames (not orthonormal bases) Thirdly, this paper gives a set of necessary and sufficient condition on the M band scaling filter for it to generate an orthonormal wavelet basis. The conditions are very similar to those obtained by Cohen [4, 8] and Lawton [27] for 2 band wavelets. This distinction between a tight frame and an orthonormal basis is quite subtle (and technical) and has been overlooked in the signal processing community. The organization of the paper is as follows. Section 2 is a tutorial overview of multirate filter bank theory, wavelet ....
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W. M. Lawton. Necessary and Sufficient Conditions for Existence of Orthornomal Wavelet Bases. Journal of Math. Physics, 1990.
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W. M. Lawton. Necessary and Sufficient Conditions for Existence of Orthornomal Wavelet Bases. Journal of Math. Physics, 1990.
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