A. J. E. M. Janssen, `Gabor representation of generalized functions', J. Math. Anal. Appl. 83 (1981) 377--394. Home/Search Document Not in Database Summary Related Articles Check |
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Amalgam Spaces and Generalized Harmonic Analysis - Feichtinger (1997) (2 citations) (Correct)
....arguments and suggested even an algorithmic approach. Larger lattice constants would not allow to expand all of L , and smaller lattice constants would not allow to have uniqueness of coefficients. Meanwhile it is known that in this critical case one has to expect a lot of problems (cf. [13], and that the algorithm as such fails to work (see [11] However, in recent years, mainly stimulated through applications in signal analysis, serious progress has been made on the mathematics of Gabor expansion, based on the insight that (modest) oversampling, i.e. the use of Gabor families ....
A.J.E.M. Janssen. Gabor representation of generalized functions. J. Math. Anal. Appl., 83:377--394, 1981.
Amalgam Spaces and Generalized Harmonic Analysis - Feichtinger (1997) (2 citations) (Correct)
....arguments and suggested even an algorithmic approach. Larger lattice constants would not allow to expand all of L 2 , and smaller lattice constants would not allow to have uniqueness of coefficients. Meanwhile it is known that in this critical case one has to expect a lot of problems (cf. [13], and that the algorithm as such fails to work (see [11] However, in recent years, mainly stimulated through applications in signal analysis, serious progress has been made on the mathematics of Gabor expansion, based on the insight that (modest) oversampling, i.e. the use of Gabor families ....
A.J.E.M. Janssen. Gabor representation of generalized functions. J. Math. Anal. Appl., 83:377--394, 1981.
Representations of Gabor frame operators - Janssen Self-citation (Janssen) (Correct)
....group of translations in the phase plane, for what we have called Gabor systems. Gabor s 1946 paper certainly did not go unnoticed by the engineering community, but it lasted until 1980 that the attention for Gabor expansions was revived through the work of Portnoff [3] Bastiaans [4] and Janssen [5]. This revival coincided, not entirely by accident, with the increasing interest in the electrical engineering community for time frequency tools, such as the Wigner Ville distribution and the short time Fourier transform. It should, however, be noted that as early as 1961 Lerner [6] presented a ....
....of Gaussian g and (ab) Gamma1 = 1. These dual functions are important since they allow one to exhibit the expansion coefficients for a particular signal f as inner products of f with the dual function shifted in a similar way as the window g itself. The mathematical analysis given by Janssen in [5] and [10] of the convergence properties of Gabor expansions and of Bastiaans dual function showed 2 that Gabor systems with Gaussian g and (ab) Gamma1 = 1 yield unstable expansions that do not properly reflect time frequency localization of the signals to be expanded. This point was also ....
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A.J.E.M. Janssen, Gabor representation of generalized functions, J. Math. Anal. Appl., 83 (1981), pp. 377--394.
Hardy's Theorem And The Short-Time Fourier Transform Of.. - Ochenig Georg Zimmermann (2001) (Correct)
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A. J. E. M. Janssen, `Gabor representation of generalized functions', J. Math. Anal. Appl. 83 (1981) 377--394.
A Group-theoretical Approach to Gabor Analysis - Feichtinger, Strohmer.. (1995) (Correct)
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A.J.E.M. Janssen. Gabor Representation of Generalized Functions. J. Math. Anal. Appl., 83:377--394, 1981.
Gabor wavelets and the Heisenberg group: Gabor Expansions .. - Feichtinger, Gröchenig (1992) (2 citations) (Correct)
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Janssen, A.J.E.M., Gabor representation of generalized functions, J.Math. Anal.Appl. 83 (1981), 377--394.
Localization of Frames - Gröchenig (Correct)
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A. J. E. M. Janssen. Gabor representation of generalized functions. J. Math. Anal. Appl., 83(2):377--394, 1981.
Topics In Harmonic Analysis With Applications To Radar And Sonar - Miller, Jr. (1991) (1 citation) (Correct)
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]A.J.E.M. Janssen, Gabor representation of generalized functions, J. of Mathematical Analysis and Applications 83 (1981), 377--394.
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