Signal processing by alternate dual Gabor frames

Arefijamaal, Ali Akbar; Zekaee, Esmaeel

doi:10.1016/j.acha.2013.06.001

Cited by 41 publications

(24 citation statements)

References 11 publications

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“…For solving this problem, frames were introduced by Duffin and Schaefer [19] and widely developed by many authors [17,18,21]. Frames have been developed rapidly in mathematics and have achieved successful applications in various areas of pure and applied sciences and engineering [5,6,[9][10][11][12].…”

Section: Motivationmentioning

confidence: 99%

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O-Cross Gram matrices with respect to $$\varvec{g}$$-frames

Arefijamaal

Shamsabadi

2019

Arab. J. Math.

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Section: Motivationmentioning

confidence: 99%

“…Frames, introduced by Duffin and Schaeffer [19] in 1952, are very important in signal processing, image processing, and many other fields [6,17,18,28]. Several generalizations of frames as continuous frames [2], fusion frames [13], and g-frames [33] have been presented.…”

Section: Introductionmentioning

confidence: 99%

O-Cross Gram matrices with respect to $$\varvec{g}$$-frames

Arefijamaal

Shamsabadi

2019

Arab. J. Math.

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“…Traditionally, the classical Gabor transforms and wavelet transforms have been used to perform time-frequency (resp. time-scale) analysis of a given function/signal in a Hilbert space, see [1][2][3]. In the last decades, generalized methods of Gabor transforms and wavelet transforms have been developed [14].…”

Section: Introductionmentioning

confidence: 99%

Finite equal norm Parseval wavelet frames over prime fields

Rahimi

Seddighi

2017

Int. J. Wavelets Multiresolut Inf. Process.

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Abstract. 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 genarator 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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“…The theoretical, computational, and applied aspects of time-frequency (Gabor) analysis have been studied at depth by many researchers and authors, see [1,2,4,7,17,18] and references therein. The mathematical theory of Gabor analysis on the real line is based on the modulations and translations of a given window signal (atom).…”

Section: Introductionmentioning

confidence: 99%

Operator-Valued Continuous Gabor Transforms over Non-unimodular Locally Compact Groups

Farashahi

2017

Mediterr. J. Math.

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Abstract. In this article, we present the abstract harmonic analysis aspects of the operator-valued continuous Gabor transform (CGT) on second countable, non-unimodular, and type I locally compact groups. We show that the operator-valued continuous Gabor transform CGT satisfies a Plancherel formula and an inversion formula. As an example, we study these results on the continuous affine group.Mathematics Subject Classification. Primary 43A30, 43A32, 43A65, 22D10.

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Signal processing by alternate dual Gabor frames

Cited by 41 publications

References 11 publications

O-Cross Gram matrices with respect to $$\varvec{g}$$-frames

O-Cross Gram matrices with respect to $$\varvec{g}$$-frames

Finite equal norm Parseval wavelet frames over prime fields

Operator-Valued Continuous Gabor Transforms over Non-unimodular Locally Compact Groups

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