Causal analytical wavelet transform

Harold H. Szu; Brian A. Telfer; Adolf W. Lohmann

doi:10.1117/12.59911

1 September 1992 Causal analytical wavelet transform

Harold H. Szu, Brian A. Telfer, Adolf W. Lohmann

Author Affiliations +

Optical Engineering, Vol. 31, Issue 9, (September 1992). https://doi.org/10.1117/12.59911

Abstract

The causal analytical wavelet transform employs exponentially decaying nonsinusoidal wideband transient bases of compact support. The basis set h_ab(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.

Citation Download Citation

Harold H. Szu, Brian A. Telfer, and Adolf W. Lohmann "Causal analytical wavelet transform," Optical Engineering 31(9), (1 September 1992). https://doi.org/10.1117/12.59911

Published: 1 September 1992

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