Intrinsic wavelet and frame applications
John J. Benedetto, Travis D. Andrews · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
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.