Phase space distribution of Gabor expansions
نویسندگان
چکیده
منابع مشابه
Phase Space Distribution of Gabor Expansions
We present an example of a complete and minimal Gabor system consisting of time-frequency shifts of a Gaussian, localized at the coordinate axes in the time-frequency plane (phase space). Asymptotically, the number of time-frequency shifts contained in a disk centered at the origin is only 2/π times the number of points from the von Neumann lattice found in the same disk. Requiring a certain re...
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We consider Gabor systems generated by a Gaussian function and prove certain classical results of Paley and Wiener on nonharmonic Fourier series of complex exponentials for the Gabor expansion. In particular, we prove a version of Plancherel-Po ́lya theorem for entire functions with finite order of growth and use the Hadamard factorization theorem to study regularity, exactness and deficienc...
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we consider gabor systems generated by a gaussian function and prove certain classical results of paley and wiener on nonharmonic fourier series of complex exponentials for the gabor expansion. in particular, we prove a version of plancherel-po ́lya theorem for entire functions with finite order of growth and use the hadamard factorization theorem to study regularity, exactness and deficienc...
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This paper is an examination of techniques for obtaining Fourier series-like expansions of finite-energy signals using so-called Gabor and wavelet expansions. These expansions decompose a given signal into time and frequency localized components. The theory of frames in Hilbert spaces is used as a criteria for determining when such expansions are good representations of the signals. Some result...
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Discrete Gabor multipliers are composed of rank one operators. We shall prove, in the case of rank one projection operators, that the generating operators for such multipliers are either Riesz bases (exact frames) or not frames for their closed linear spans. The same dichotomy conclusion is valid for general rank one operators under mild and natural conditions. This is relevant since discrete G...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2009
ISSN: 1063-5203
DOI: 10.1016/j.acha.2008.07.005