Positive Sampling in Wavelet Subspaces
نویسندگان
چکیده
منابع مشابه
Two-channel sampling in wavelet subspaces
We develop two-channel sampling theory in the wavelet subspace V1 from the multi resolution analysis {Vj}j∈Z. Extending earlier results by G. G. Walter [11], W. Chen and S. Itoh [2] and Y. M. Hong et al [5] on the sampling theory in the wavelet or shift invariant spaces, we find a necessary and sufficient condition for two-channel sampling expansion formula to hold in V1. 1 Indroduction The cla...
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where f ( w ) is the Fourier transform of f ( t ) defined by f ( w ) = J, f ( t )e-*”*dt . Unfortunately it is not appropriate for nonband-limited signals. However if we let y = 2 m ~ , m € 2, this problem can be viewed as a special case of sampling in wavelet subspaces with p(t) = sin?rt/nt playing the role of scaling function of MRA {Vm = W ( ~ ( 2 ~ t n},},. Realizing these properties, Walte...
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Following our former works on regular sampling in wavelet subspaces, the paper provides two algorithms to estimate the truncation error and aliasing error respectively when the theorem is applied to calculate concrete signals. Furthermore the shift sampling case is also discussed. Finally some important examples are calculated to show the algorithm. key words: sampling, scaling function, wavele...
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The Zak transform is used for generalizing a sampling theorem of G. Walter for wavelet subspaces. Cardinal series based on signal samples f(a + n), n E 2 with a possibly unequal to 0 (Walter’s case) are considered. The condition number of the sampling operator and worst-case aliasing errors are expressed in terms of Zak transforms of scaling function and wavelet. This shows that the stability o...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2002
ISSN: 1063-5203
DOI: 10.1006/acha.2001.0368