Intrinsic wavelet and frame applications

John J. Benedetto; Travis D. Andrews

doi:10.1117/12.889119

12 May 2011 Intrinsic wavelet and frame applications

John J. Benedetto, Travis D. Andrews

Proceedings Volume 8058, Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering IX; 805802 (2011) https://doi.org/10.1117/12.889119
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

Abstract

There are intrinsic wavelet applications, by which we mean mathematical modeling of a physical phenomenon in which wavelet theory is the most natural quantitative means of explaining the phenomenon. This is not the same as the invaluable use of dyadic wavelets, say, as a tool with which to zoom-in or -out with regard to multi-scale phenomena. An example of an intrinsic wavelet application is wavelet auditory modeling (WAM). WAM is analyzed herein, and a natural excursion, one of many possibilities, is taken from WAM to applications of finite frames. This path includes the role of the Discrete Fourier Transform (DFT) in WAM, the emergence of DFT frames, and their use in analyzing Σ▵ quantization, which itself is a staple in audio engineering as well as in a host of other applications.

Citation Download Citation

John J. Benedetto and Travis D. Andrews "Intrinsic wavelet and frame applications", Proc. SPIE 8058, Independent Component Analyses, Wavelets, Neural Networks, Biosystems, and Nanoengineering IX, 805802 (12 May 2011); https://doi.org/10.1117/12.889119

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