Approximation of the Fourier Transform and the Dual Gabor Window

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Wiener amalgam spaces for the fundamental identity of Gabor analysis (2005, methodology): “f(x)g(ω)e−2πix·ω for z = (x,ω) ∈ R2d. It is a very popular time-frequency representation in engineering, [HM01, Gr04]. An application of Theorem 4.2 yields a generalization of a formula of Kaiblinger [Ka05] which also established a connection to the Rihaczek distribution. Proposition 4.4. Let f,g be”
Modulation Spaces: Looking Back and Ahead (2006, unknown): “[143] N.”
Gabor Frames in Finite Dimensions (2013, background): “The relationship between Gabor systems on the real line, on the integers, and on cyclic groups are studied based on sampling and periodization arguments in [54, 55, 69, 86, 87].”
Finite Discrete Gabor Analysis (2007, methodology): “Kaiblinger showed in [62] that this is indeed possible.”
Banach Gelfand Triples for Gabor Analysis (2008, background): “for some real σ> 0. The Gaussian generates a Gabor frame if and only if αβ 31 , 35, 38, 39].”