H. G. Feichtinger, K. Grochenig, and D. Walnut, Wilson bases and modulation spaces, Math. Nachr. 155 (1992), 7--17.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....analysis can be applied. Furthermore, we want to mention the application of best basis algorithms for the adaptive choice of the window size in [20, 23, 45, 48] and the construction of bivariate bases in [11, 16, 50, 51] Results on the approximation with local trigonometric bases can be found in [14, 15, 29, 33]. For the design of optimized window functions we refer to [12, 14, 15, 36, 41] To reduce blocking e ects local trigonometric bases have been applied in speech processing [45] and image compression [1, 2, 35, 39] Furthermore, ecient algorithms based on the fast Fourier transform (FFT) have been ....

H. G. Feichtinger, K. Grochenig, and D. Walnut. Wilson bases and modulation spaces. Math. Nachr., 155:7-17, 1992.

....result for Wilson bases with window functions of arbitrary shape and Sobolev spaces H # (R) # # R. The proofs of these statements are completely di#erent from the proofs in [6] In particular, we show that Wilson bases are unconditional bases if the window function is su#ciently smooth. In [15], Feichtinger, Grochenig and Walnut showed that orthonormal Wilson bases are unconditional bases for modulation spaces and thus for the Sobolev spaces H # (R) if the window function is contained in the Schwartz space S(R) i.e. infinitely times di#erentiable with exponential decay. ....

H. G. Feichtinger, K. Grochenig, and D. Walnut. Wilson bases and modulation spaces. Math. Nachr., 155:7--17, 1992.

....analysis can be applied. Furthermore, we want to mention the application of best basis algorithms for the adaptive choice of the window size in [20, 23, 45, 48] and the construction of bivariate bases in [11, 16, 50, 51] Results on the approximation with local trigonometric bases can be found in [14, 15, 29, 33]. For the design of optimized window functions we refer to [12, 14, 15, 36, 41] To reduce blocking e#ects local trigonometric bases have been applied in speech processing [45] and image compression [1, 2, 35, 40] Furthermore, e#cient algorithms based on the fast Fourier transform (FFT) have been ....

H. G. Feichtinger, K. Grochenig, and D. Walnut. Wilson bases and modulation spaces. Math. Nachr., 155:7--17, 1992.

....of special cases) instead the unconditional bases are furnished by Gabortype expansions in windowed sinusoids. Daubechies, Jaffard, and Journ e have developed special windows which give orthonormal Gabor type expansions; they call these Wilson bases [4] Feichtinger, Grochenig, and Walnut [17] have shown that these are unconditional bases of Modulation spaces. From the perspective of this paper, Orthonormal Wilson bases are near optimal for representing objects in Modulation spaces. Do modulation spaces describe practically important phenomena Certain signals consist of superpositions ....

Feichtinger, H.G., Grochenig, K., and Walnut, D. (1992) Wilson Bases and Modulation Spaces. Manuscript.

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H. G. Feichtinger, K. Grochenig, and D. Walnut, Wilson bases and modulation spaces, Math. Nachr., 155, 7--17, 1992.

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Feichtinger, H.G.,K. Grochenig and D. Walnut, Wilson bases and modulation spaces. Math.Nachrichten, to appear 1991.

....lter banks. 1. INTRODUCTION The Gabor expansion [1] 9] is an important linear signal representation. Unfortunately, there do not exist orthonormal Gabor function sets (Weyl Heisenberg sets) with good localization in both time and frequency [6, 7] The recently proposed Wilson expansion [10] [12] is a simple variation on the Gabor expansion that overcomes this drawback. So far, only continuous time Wilson bases have been considered [10] 12] This paper introduces discrete time Wilson sets and frames with critical sampling and oversampling. Extending the derivation of orthonormal ....

....Gabor function sets (Weyl Heisenberg sets) with good localization in both time and frequency [6, 7] The recently proposed Wilson expansion [10] 12] is a simple variation on the Gabor expansion that overcomes this drawback. So far, only continuous time Wilson bases have been considered [10] [12]. This paper introduces discrete time Wilson sets and frames with critical sampling and oversampling. Extending the derivation of orthonormal continuoustime Wilson bases from tight Weyl Heisenberg (WH) frames [10] we show that discrete time Wilson sets frames oversampled by a factor K (K odd) can ....

H. G. Feichtinger, K. Grochenig, and D. Walnut, \Wilson bases and modulation spaces," Math. Nachrichten, Vol. 155, 1992, pp. 7-17.

....q s ) g 2 p ) The continuity and invertibility of S and S 1=2 on M s p;q (R) for ab = 1=2 says that these operators preserve smoothness and decay as measured by membership in the spaces M s p;q . It has been shown that unconditional bases of Wilson type exist for the modulation spaces [FGW92]. The continuity and invertibility of S and S 1=2 on the modulation spaces has been used in [GW92] to construct sets of sampling and interpolation in the Bargmann Fock spaces of entire functions. A general construction that includes many examples of Wilson bases as well as wavelet bases are the ....

H. G. Feichtinger, K. Gr¨ochenig, and D. Walnut, Wilson bases and modulation spaces, Math. Nachr. 155 (1992), 7--17.

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H. G. Feichtinger, K. Grochenig, and D. Walnut, Wilson bases and modulation spaces, Math. Nachr. 155 (1992), 7--17.

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H. G. Feichtinger, K. Grochenig, and D. Walnut. Wilson bases and modulation spaces. Math. Nachr., 155:7--17, 1992.

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