𝔖 Bobbio Scriptorium
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The joy of secants

✍ Scribed by Gray, Jeremy


Book ID
109718697
Publisher
Nature Publishing Group
Year
1998
Tongue
English
Weight
216 KB
Volume
394
Category
Article
ISSN
0028-0836

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We show that (g 2 , a, b) is a Gabor frame when a > 0, b > 0, ab < 1, and g 2 (t) = ( 1 2 πγ ) 1/2 (cosh πγ t) -1 is a hyperbolic secant with scaling parameter Ξ³ > 0. This is accomplished by expressing the Zak transform of g 2 in terms of the Zak transform of the Gaussian g 1 (t) = (2Ξ³ ) 1/4 exp(-πγ