Multiplicative and zero-crossing representations of signals

Anca Deliu; Michael L. Hilton; Bjorn D. Jawerth; Prasanjit Panda; Wim Sweldens

doi:10.1117/12.188789

11 October 1994 Multiplicative and zero-crossing representations of signals

Anca Deliu, Michael L. Hilton, Bjorn D. Jawerth, Prasanjit Panda, Wim Sweldens

Proceedings Volume 2303, Wavelet Applications in Signal and Image Processing II; (1994) https://doi.org/10.1117/12.188789
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

The implicit sampling theorem of Bar-David gives a representation of band limited functions using their crossings with a cosine function. This cosine function is chosen such that its difference with the original function has sufficient zero crossings for a unique representation. We show how, on an interval, this leads to a multiplicative representation involving a Riesz product. This provides an alternative to the classic additive Fourier series. We discuss stability and implementation issues. Since we have an explicit reconstruction formula, there is no need for an iterative algorithm.

Citation Download Citation

Anca Deliu, Michael L. Hilton, Bjorn D. Jawerth, Prasanjit Panda, and Wim Sweldens "Multiplicative and zero-crossing representations of signals", Proc. SPIE 2303, Wavelet Applications in Signal and Image Processing II, (11 October 1994); https://doi.org/10.1117/12.188789

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