Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration

Erden, M.F.; Kutay, M. Alper; Özaktaş, Haldun M.

doi:10.1109/78.757244

Cited by 82 publications

(53 citation statements)

References 18 publications

(27 reference statements)

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“…For this purpose, various time-frequency processing techniques (e.g. Hlawatsch et al, , 2000Erden et al, 1999;Hlawatsch and Kozek, 1994;McHale and Boudreaux-Bartels, 1993; Boudreaux-Bartels and Parks, 1986) can be used. In the following, results based on the time-frequency domain incision technique (Erden et al, 1999) will be presented.…”

Section: Application Of Tfca To the Analysis Of Multi-component Signalsmentioning

confidence: 99%

Time–frequency component analyser and its application to brain oscillatory activity

Özdemir

Karakaş

Çakmak

et al. 2005

Journal of Neuroscience Methods

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Currently, event-related potential (ERP) signals are analysed in the time domain (ERP technique) or in the frequency domain (Fourier analysis and variants). In techniques of time-domain and frequency-domain analysis (short-time Fourier transform, wavelet transform) assumptions concerning linearity, stationarity, and templates are made about the brain signals. In the time-frequency component analyser (TFCA), the assumption is that the signal has one or more components with non-overlapping supports in the time-frequency plane. In this study, the TFCA technique was applied to ERPs. TFCA determined and extracted the oscillatory components from the signal and, simultaneously, localized them in the time-frequency plane with high resolution and negligible cross-term contamination. The results obtained by means of TFCA were compared with those obtained by means of other commonly used techniques of ERP analysis, such as bilinear time-frequency distributions and wavelet analysis. It is suggested that TFCA may serve as an appropriate tool for capturing the localized ERP components in the time-frequency domain and for studying the intricate, frequency-based dynamics of the human brain.

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Section: Application Of Tfca To the Analysis Of Multi-component Signalsmentioning

confidence: 99%

Time–frequency component analyser and its application to brain oscillatory activity

Özdemir

Karakaş

Çakmak

et al. 2005

Journal of Neuroscience Methods

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“…It is possible to further generalize these ®ltering con®gurations by using parallel and series arrangements together; such systems have been called generalized ®ltering circuits [1,2]. Fractional Fourier transform has found many applications in optics in general [8] and fractional Fourier transform-based ®ltering circuits have found applications in optical and digital signal and image restoration, signal and system synthesis, synthesis of mutual intensity distributions, and fast implementation of shift-variant linear systems [1,2,5,7].…”

mentioning

confidence: 99%

“…[2,5,7] fractional Fourier transformbased ®ltering con®gurations have been used for synthesizing linear space-variant systems, represented by some matrix T. It was shown that for many such systems encountered in various applications, it is possible to approximate the system with a multi-stage or multi-channel con®guration with acceptable mean square error, by using a small or moderate number (M) of stages or channels. Since the cost of implementing the fractional Fourier transform (optically or digitally) is similar to the cost of implementing the ordinary Fourier transform, this leads to a fast implementation of the space-variant system in question.…”

mentioning

confidence: 99%

“…1(e) and (f)). In multi-stage ®ltering [2,5] the input is ®rst transformed into the a 1 th domain, where it is multiplied by a ®lter h 1 . The result is then transformed back into the original domain.…”

mentioning

confidence: 99%

“…The problem of ®nding the optimal ®lter coe cients, given the transform orders has been solved in Refs. [2,4,5] using a minimum mean square error approach. On the other hand, the problem of optimizing multiple orders has not yet been addressed, and in most cases the orders have been chosen uniformly.…”

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confidence: 99%

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Image representation and compression with the fractional Fourier transform

Yetik

Kutay

Özaktaş

2001

Optics Communications

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We discuss the application of fractional Fourier transform-based ®ltering con®gurations to image representation and compression. An image can be approximately represented (and stored or transmitted) as the coe cients of the minimum mean square ®ltering con®guration approximating the image matrix. An order of magnitude compression is possible with moderate errors with the raw method. While inferior to commonly available compression algorithms, the results presented correspond to the basic method without any re®nement or combination with other techniques, suggesting that the approach may hold promise for future development. Regardless of its practical usefulness, the fact that the information inherent in an image can be decomposed or factored into fractional Fourier domains is of considerable conceptual signi®cance. The information contained in the image is distributed to the di erent domains in an unequal way, making some domains more dispensible than others in representing the image. Ó 2001 Published by Elsevier Science B.V.

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Paley–Wiener theorems and uncertainty principles for the windowed linear canonical transform

Kou

Zhang

2012

Math Methods in App Sciences

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Communicated by T. QianIn a recent paper, the authors have introduced the windowed linear canonical transform and shown its good properties together with some applications such as Poisson summation formulas, sampling interpolation, and series expansion. In this paper, we prove the Paley-Wiener theorems and the uncertainty principles for the (inverse) windowed linear canonical transform. They are new in literature and has some consequences that are now under investigation.

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Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration

Cited by 82 publications

References 18 publications

Time–frequency component analyser and its application to brain oscillatory activity

Time–frequency component analyser and its application to brain oscillatory activity

Image representation and compression with the fractional Fourier transform

Paley–Wiener theorems and uncertainty principles for the windowed linear canonical transform

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