Wave packet frames on local fields of positive characteristic

Abdullah, Abdullah; Shah, Firdous A.

doi:10.1016/j.amc.2014.09.130

Cited by 13 publications

(2 citation statements)

References 24 publications

(23 reference statements)

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“…On the other hand, Behera and Jahan [1] have constructed biorthogonal wavelets on local fields of positive characteristic and showed that if φ andφ are the dual scaling functions associated with dual MRAs on local fields of positive characteristic such that their translates are biorthogonal, then the corresponding wavelet families are also biorthogonal. More results in this direction can also be found in [8,[18][19][20] and the references therein.…”

Section: Introductionmentioning

confidence: 69%

Construction of biorthogonal wavelet packets on local fields of positive characteristic

Shah¹,

Bhat²

2016

Turk J Math

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Orthogonal wavelet packets lack symmetry which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality is replaced by the biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of the Fourier transforms. We also show how to obtain several new Riesz bases of the space L 2 (K) by constructing a series of subspaces of these wavelet packets. Finally, we provide the algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets.

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Section: Introductionmentioning

confidence: 69%

Construction of biorthogonal wavelet packets on local fields of positive characteristic

Shah¹,

Bhat²

2016

Turk J Math

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“…As far as the characterization of wavelet frames on local fields is concerned, Shah and Abdullah [27] have established a complete characterization of tight wavelet frames on local fields by virtue of two basic equations in the frequency domain and proved how to construct an orthonormal wavelet basis for L 2 (K). More results in this direction can also be found in [26,28] and the references therein. In the study of shift invariant systems and frames, several authors have made extensive use of the so called bracket product.…”

Section: Introductionmentioning

confidence: 71%