Abstract
A wavelet auditory model (WAM™) is formulated. The implementation of WAM™ for speech compression depends on an irregular sampling theorem and an analysis of time-scale data. The time-scale plane for WAM™ is analogous to Gabor’s dissection of the information plane by means of the uncertainty principle inequality. Generalizations of this inequality lead to other dissections of the information plane; and their proofs depend on weighted Fourier transform norm inequalities. These inequalities give rise to definitions of the Fourier transform on weighted Lebesgue spaces; the definitions are sometimes necessarily different than the usual one because of the behavior of the weights.
This work was supported by Prometheus Inc., under DARPA Contract DAA-H01-91-CR212.
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Dedicated to the memory of Bruce Heath.
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Benedetto, J.J. (1994). From a wavelet auditory model to definitions of the Fourier transform. In: Byrnes, J.S., Byrnes, J.L., Hargreaves, K.A., Berry, K. (eds) Wavelets and Their Applications. NATO ASI Series, vol 442. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1028-0_1
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DOI: https://doi.org/10.1007/978-94-011-1028-0_1
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