Wavelet-based cosine crossings of signals

The periodic Bar-David (1974) sampling theorem provides an implicit representation of band limited signals using their crossings with a cosine function to form a multiplicative representation involving a Riesz product. The cosine crossings form a unique and stable representation of the signal. We incorporate the wavelet transform into the cosine crossing representation and show that they may be used to compactly represent overcomplete signal expansions.