1 September 1992 Causal analytical wavelet transform
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Optical Engineering, 31(9), (1992). doi:10.1117/12.59911
Abstract
The causal analytical wavelet transform employs exponentially decaying nonsinusoidal wideband transient bases of compact support. The basis set hab(t) = h[(t- b)/a]√a is called daughter wavelets, which are constructed from a causal analytical mother wavelet h(t) by means of the dilation parameter a and the translation parameter b. We show that a causal (i.e., zero valued before signal arrives) and analytical mother wavelet still guarantees completeness. This permits the selection of mother wavelets that better match causal analytical input signals. An optical architecture is described for real-time implementation.
Harold H. Szu, Brian A. Telfer, Adolf W. Lohmann, "Causal analytical wavelet transform," Optical Engineering 31(9), (1 September 1992). http://dx.doi.org/10.1117/12.59911
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KEYWORDS
Wavelets

Wavelet transforms

Signal to noise ratio

Signal analyzers

Fourier transforms

Signal detection

Acousto-optics

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