Multiplicative and zero crossing representations of signals
Deliu, Anca Hilton, Michael L. Jawerth, Bjorn D. Panda, Prasanjit Sweldens, Wim #
Mathematical Imaging: Wavelet Approximations in Signal and Image Processing II pages:400-410
SPIE location:San Diego, California date:27-29 July 1994
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.