classical wavelet transforms over finite fields
Authors
abstract
this article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. we present a concrete formulation for the frobenius norm of the classical wavelet transforms over finite fields. it is shown that each vector defined over a finite field can be represented as a finite coherent sum of classical wavelet coefficients.
similar resources
Classical Wavelet Transforms over Finite Fields
This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...
full textClassical wavelet systems over finite fields
This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...
full textclassical wavelet systems over finite fields
this article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. it is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...
full textHartley transforms over finite fields
A general f ramework is presented for constructing transforms in the field of the input which have a convolutionlike property. The construction is carried out over finite fields, but is shown to be valid over the real and complex fields as well. It is shown that these basefield transforms can be v iewed as “projections” of the discrete Fourier transform @IT) and that they exist for all lengths ...
full textStructure of finite wavelet frames over prime fields
This article presents a systematic study for structure of finite wavelet frames over prime fields. Let $p$ be a positive prime integer and $mathbb{W}_p$ be the finite wavelet group over the prime field $mathbb{Z}_p$. We study theoretical frame aspects of finite wavelet systems generated by subgroups of the finite wavelet group $mathbb{W}_p$.
full textTheory of wavelet transform over finite fields
In this paper, we develop the theory of the wavelet transform over Galois elds. To avoid the limitations inherent in the number theoretic Fourier transform over nite elds, our wavelet transform relies on a basis decomposition in the time domain rather than in the frequency domain. First, we characterize the in nite dimensional vector spaces for which an orthonormal basis expansion of any sequen...
full textMy Resources
Save resource for easier access later
Journal title:
journal of linear and topological algebra (jlta)جلد ۴، شماره ۰۴، صفحات ۲۴۱-۲۵۷
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023