Some applications of wavelets to physics
A thorough description of a fast wavelet transform algorithm (FWT) and its inverse (IFWT) are given. The effects of noise in the wavelet transform are studied, in particular the effects on signal reconstruction. A model for additive white noise on the coefficients is presented along with two methods that can help to suppress the effects of noise corruption of the signal. Problems of improper sampling are studied, including the propagation of uncertainty through the FWT and IFWT. Interpolation techniques and data compression are also studied. The FWT and IFWT are generalized for analysis of two dimensional images. Methods for edge detection are discussed as well as contrast improvement and data compression. Finally, wavelets are applied to electromagnetic wave propagation problems. Formulas relating the wavelet and Fourier transforms are given, and expansions of time-dependent electromagnetic fields using both fixed and moving wavelet bases are studied.
- Research Organization:
- Missouri Univ., Columbia, MO (United States)
- OSTI ID:
- 7161829
- Country of Publication:
- United States
- Language:
- English
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