Finite equal norm Parseval wavelet frames over prime fields

In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator, we derive a locally-scaled version of the DFT of system generator and obtain a finite equal-norm Parseval wavelet frame over prime fields. We also give a characterization of all multiplicative subgroups of the cyclic multiplicative group, for which the associated wavelet systems form frames. Finally, we present some concrete examples as applications of our results.

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A New Characterization of Finite Prime Fields

Canadian Mathematical Bulletin ◽

10.4153/cmb-1968-043-8 ◽

1968 ◽

Vol 11 (3) ◽

pp. 381-382 ◽

Cited By ~ 2

Author(s):

Carlton J. Maxson

Keyword(s):

Multiplicative Group ◽

Near Field ◽

Finite Case ◽

Prime Fields

Let N ≡ <N, +,.> be a (right) near-ring with 1 (we say N is a unitary near-ring)[1] and recall that a near-field is a unitary near-ring in which <N - {0}, . > is a multiplicative group. In [2], Beidelman characterizes near-fields as those unitary near-rings without non-trivial N-subgroups. We show that in the finite case this absence of non-trivial N-subgroups is equivalent to the absence of non-trivial left ideals.

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Characterization of matrix Fourier multipliers for A-dilation Parseval multi-wavelet frames

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691315500514 ◽

2015 ◽

Vol 13 (06) ◽

pp. 1550051

Author(s):

Yongdong Huang ◽

Fengjuan Zhu

Keyword(s):

Fourier Multipliers ◽

Frame Theory ◽

Wavelet Frame ◽

Wavelet Frames ◽

Integral Matrix ◽

Numerical Examples ◽

Basic Properties ◽

New Formula

Let [Formula: see text] be a [Formula: see text] expansive integral matrix with [Formula: see text]. This paper investigates matrix Fourier multipliers for [Formula: see text]-dilation Parseval multi-wavelet frames, which are [Formula: see text] matrices with [Formula: see text] function entries, map [Formula: see text]-dilation Parseval multi-wavelet frames of length [Formula: see text] to [Formula: see text]-dilation Parseval multi-wavelet frames of length [Formula: see text], where [Formula: see text]. We completely characterize all matrix Fourier multipliers for [Formula: see text]-dilation Parseval multi-wavelet frames and construct several numerical examples. As Fourier wavelet frame multiplier, matrix Fourier multipliers can be used to derive new [Formula: see text]-dilation Parseval multi-wavelet frames and can help us better understand the basic properties of frame theory.

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The Characterization of a Pair of Canonical Frames Generated by Several Compactly Supported Functions

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.1135 ◽

2010 ◽

Vol 439-440 ◽

pp. 1135-1140

Author(s):

Jun Qiu Wang ◽

Jian Guo Wang

Keyword(s):

Scaling Functions ◽

Wavelet Frame ◽

Wavelet Frames ◽

The Past ◽

Single Function ◽

Dual Wavelet Frames ◽

Popular Subject ◽

Compactly Supported Functions ◽

Dual Wavelet

Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function.

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On Parseval Wavelet Frames via Multiresolution Analyses in

Canadian Mathematical Bulletin ◽

10.4153/s0008439519000341 ◽

2019 ◽

Vol 63 (1) ◽

pp. 157-172

Author(s):

A. San Antolín

Keyword(s):

Fourier Transform ◽

Multiresolution Analysis ◽

Extension Principle ◽

Refinable Functions ◽

Wavelet Frames ◽

Approximate Continuity ◽

Reducing Subspaces ◽

The Fourier Transform ◽

Frame Multiresolution Analysis

AbstractWe give a characterization of all Parseval wavelet frames arising from a given frame multiresolution analysis. As a consequence, we obtain a description of all Parseval wavelet frames associated with a frame multiresolution analysis. These results are based on a version of Oblique Extension Principle with the assumption that the origin is a point of approximate continuity of the Fourier transform of the involved refinable functions. Our results are written for reducing subspaces.

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Characterization of water-soluble organic compounds in ambient aerosol using ultrahigh-resolution elctrospray ionization fourier transform ion cyclotron resonance mass spectrometry.

10.37099/mtu.dc.etd-restricted/72 ◽

2012 ◽

Author(s):

Parichehr Saranjampour

Keyword(s):

Mass Spectrometry ◽

Fourier Transform ◽

Organic Compounds ◽

Cyclotron Resonance ◽

Water Soluble ◽

Ion Cyclotron Resonance ◽

Ultrahigh Resolution ◽

Ambient Aerosol ◽

Ion Cyclotron

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Infrared Spectroscopy Characterization of Marine Shells

MRS Proceedings ◽

10.1557/proc-711-hh3.49.1 ◽

2001 ◽

Vol 711 ◽

Author(s):

Octavio Gomez-Martinez ◽

Daniel H. Aguilar ◽

Patricia Quintana ◽

Juan J. Alvarado-Gil ◽

Dalila Aldana ◽

...

Keyword(s):

Fourier Transform ◽

Infrared Spectroscopy ◽

Crassostrea Virginica ◽

Thermal Treatments ◽

Vibration Modes ◽

Lattice Vibrations ◽

Vibration Frequencies ◽

Mussel Shells ◽

Carbonate Lattice

ABSTRACTFourier Transform infrared spectroscopy has been employed to study the shells of two kind of mollusks, American oysters (Crassostrea virginica) and mussels (Ischadium recurvum). It is shown that it is possible to distinguish the different calcium carbonate lattice vibrations in each case, mussel shells present aragonite vibration frequencies, and the oyster shells present those corresponding to calcite. The superposition, shift and broadening of the infrared bands are discussed. Changes in the vibration modes due to successive thermal treatments are also reported.

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