Journal ArticleDOI
Fast discrete Fourier transform on local fields of positive characteristic
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For the discrete Fourier transform with respect to the system of characters of a local field with positive characteristic, a fast algorithm is proposed and the complexity of the algorithm is found.Abstract:
For the discrete Fourier transform with respect to the system of characters of a local field with positive characteristic, we propose a fast algorithm. We find the complexity of the algorithm.read more
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Proceedings ArticleDOI
The Research of Qualification Detection of Cable Joint Solder Joint Based on DCNN
TL;DR: In view of the problems of low recognition rate, slow detection speed and poor generalization of existing traditional detection methods, a DCNN-based method for detecting the solder joint qualification of cable joints is proposed, which has higher practical application value than other traditional algorithms.
Journal ArticleDOI
Fast Discrete Fourier Transform on Local Fields of Zero Characteristic
S. F. Lukomskii,A. M. Vodolazov +1 more
TL;DR: For the discrete Fourier transform with respect to the system of characters of a local field with zero characteristic, a fast algorithm is proposed and the complexity of the algorithm is found.
Journal ArticleDOI
On p-adic tight wavelet frames
TL;DR: In this paper , a simple method to construct step mask and corresponding step wavelet functions that generate tight wavelet frames on the field Qp of p-adic numbers is proposed.
References
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Book
Fourier Analysis on Local Fields.
TL;DR: This book presents a development of the basic facts about harmonic analysis on local fields and the "n"-dimensional vector spaces over these fields and focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications.
Journal ArticleDOI
Multiresolution analysis on local fields
TL;DR: In this article, the fundamental framework of multiresolution on local field in wavelet analysis is established and the concept of integral periodicity of a function on L2(K) is defined.
Journal ArticleDOI
Multiresolution analysis on local fields and characterization of scaling functions
Biswaranjan Behera,Qaiser Jahan +1 more
TL;DR: In this paper, it is shown that the discrete translates of a single function in the core subspace of the MRA form a Riesz basis instead of an orthonormal basis and that the intersection triviality condition in the definition of MRA follows from the other conditions of an MRA.
Journal ArticleDOI
Wavelet packets and wavelet frame packets on local fields of positive characteristic
Biswaranjan Behera,Qaiser Jahan +1 more
TL;DR: In this article, the concepts of multiresolution analysis (MRA) and wavelets can be generalized to a local field K of positive characteristic, and the wavelet packets associated with such MRAs are constructed.
Journal ArticleDOI
Characterization of wavelets and MRA wavelets on local fields of positive characteristic
Biswaranjan Behera,Qaiser Jahan +1 more
TL;DR: In this article, a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi-affine frames is provided, and all wavelets associated with a multiresolution analysis on such a local field are also characterized.
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