Multiplier Theorems for the Short-Time Fourier Transform

Weisz, Ferenc

doi:10.1007/s00020-007-1546-5

Cited by 13 publications

(11 citation statements)

References 26 publications

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“…The results in [5] enlarge the ones in the literature, concerning L p spaces [36], potential and Sobolev spaces [2], modulation spaces [20,30,31]. Other boundedness results for STFT multipliers on L p , modulation, and Wiener amalgam spaces are contained in [33].…”

Section: Introductionmentioning

confidence: 63%

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Sharp continuity results for the short-time Fourier transform and for localization operators

Cordero

Nicola

2010

Monatsh Math

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Abstract. We completely characterize the boundedness on L p spaces and on Wiener amalgam spaces of the short-time Fourier transform (STFT) and of a special class of pseudodifferential operators, called localization operators. Precisely, a well-known STFT boundedness result on L p spaces is proved to be sharp. Then, sufficient conditions for the STFT to be bounded on the Wiener amalgam spaces W (L p , L q ) are given and their sharpness is shown. Localization operators are treated similarly. Using different techniques from those employed in the literature, we relax the known sufficient boundedness conditions for localization operators on L p spaces and prove the optimality of our results. More generally, we prove sufficient and necessary conditions for such operators to be bounded on Wiener amalgam spaces.

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Section: Introductionmentioning

confidence: 63%

“…We also recall their employment as approximation of pseudodifferential operators (wave packets) [11,22]. Localization operators are also called Toeplitz operators (see, e.g., [13]) or short-time Fourier transform multipliers [20,33]. Their definition can be given by means of the STFT as follows.…”

Section: Introductionmentioning

confidence: 99%

Sharp continuity results for the short-time Fourier transform and for localization operators

Cordero

Nicola

2010

Monatsh Math

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“…The effectiveness of the WFT is a result of its providing a unique representation for the signals in terms of the windowed Fourier kernel. Recently, some authors [2][3][4][5][6][7] have extensively studied the WFT and its properties from a mathematical point of view. Nowadays the WFT has effectively been applied in many fields of science and engineering, such as image analysis and image compression, object and pattern recognition, computer vision, optics, and filter banks (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Real clifford windowed Fourier transform

Bahri

Adji

Zhao

2011

Acta. Math. Sin.-English Ser.

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We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform (WFT) and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.

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“…One method to overcome such a problem is the windowed Fourier transform (WFT). Recently, some authors [6,9,23] have extensively studied the WFT and its properties from a mathematical point of view. In [17,24] the WFT has been successfully applied as a tool of spatial-frequency analysis which is able to characterize the local frequency at any location in a fringe pattern.…”

Section: Introductionmentioning

confidence: 99%