Modified wavelets that accommodate causality

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

doi:10.1117/12.138463

1 October 1992 Modified wavelets that accommodate causality

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

Proceedings Volume 1705, Visual Information Processing; (1992) https://doi.org/10.1117/12.138463
Event: Aerospace Sensing, 1992, Orlando, FL, United States

Abstract

The Wavelet Transform (WT) employs nonsinusoidal bases of compact support. The basis sets g_ab(t) equals g((t-b)/a)(root)a are called daughter wavelets, which are constructed from a mother wavelet g(t) by means of the dilation operation with parameters a and the translation operation with parameter b. Normally, the mother wavelet g(t) is required to be an even function with (integral) ₀^INFdfG(f)²/f<(infinity) , to guarantee that the basis set is complete. We show that the mother wavelet can be causal instead of even and still guarantee completeness. This allows mother wavelets to be selected that better match causal input signals. A parallel optical WT architecture is sketched.

Citation Download Citation

Harold H. Szu, Brian A. Telfer, and Adolf W. Lohmann "Modified wavelets that accommodate causality", Proc. SPIE 1705, Visual Information Processing, (1 October 1992); https://doi.org/10.1117/12.138463

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