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The construction of single wavelets in d-dimensions

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Abstract

Sets K in d-dimensional Euclidean space are constructed with the property that the inverse Fourier transform of the characteristic function 1 K is a single dyadic orthonormal wavelet. The construction is characterized by its generality in the procedure, by its computational implementation, and by its simplicity. The general case in which the inverse Fourier transforms of the characteristic functions 1K 1, ..., 1K L are a family of orthonormal wavelets is treated in [27].

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  1. Department of Mathematics, University of Maryland, 20742, College Park, MD

    J. J. Benedetto & M. Leon

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  1. J. J. Benedetto
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  2. M. Leon
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Correspondence to J. J. Benedetto.

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Benedetto, J.J., Leon, M. The construction of single wavelets in d-dimensions. J Geom Anal 11, 1–15 (2001). https://doi.org/10.1007/BF02921951

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