To continue my howling in the wilderness, what the *intrepid follower of links* would find from the lecture on Meyer's[φ] wavelets is that wavelet transforms offer up much better fidelity than Fourier's, with fewer artifacts, better data compression, and from fewer resources. Why wouldn't nature prefer it? Again, perhaps because nature found yet a more suitable transform than either.
FWIW, waveguides offer up a third instance of impedance matching, that of characteristic impedance. [φ] The first part of the lecture is also interesting to the *lover of complexity* as Meyer was the first to realize that quasi-crystals, and aperiodic tilings more generally, can be manifest as projections of higher-dimensional periodic structures. Tao, in passing, mentions how the Fourier spectrum, OTOH, obscures the details of aperiodic structures this way, as they do not look different than the periodic case. OTO this detail provided insight into the connection between these higher dimensional periodics and their lower dimension aperiodic representations. -- Sent from: http://friam.471366.n2.nabble.com/ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: http://friam.471366.n2.nabble.com/
