On the smoothness of dual windows for Gabor windows supported on [−1, 1]

Jakob Lemvig, Kamilla Haahr Nielsen

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Abstract

We study Gabor frames of the form {e2πibm·g(· − ak)}m,k∈Z generated by n times differentiable windows g that are non-zero on an open interval of length L > 0 with translation parameter a = L/2 and modulation parameter b ∈ (0, 2/L). We first review recent explicit constructions of all dual windows with sufficiently short support by the authors. We then show that the obtainable smoothness of dual windows depends on the location of singularities of g. Our proof yields an explicit construction procedure of smooth dual windows once the singularities of g avoid the specified locations.
Original languageEnglish
Title of host publicationProceedings of 13th SampTA (Sampling Theory and Applications)
Number of pages4
Publication date2019
Publication statusPublished - 2019
Event2019 13th International conference on Sampling Theory and Applications - University of Bordeaux, France
Duration: 8 Jul 201912 Jul 2019

Conference

Conference2019 13th International conference on Sampling Theory and Applications
CountryFrance
CityUniversity of Bordeaux
Period08/07/201912/07/2019

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