Shift properties of discrete W transforms and real time discrete W analyzers

This brief presents the shift properties of discrete W transforms (DWT) which leads to several new approaches for computing the running DWT. Both the first- and the second-order shift properties of DWTs are derived, and the architecture of real time DWT analyzers are proposed based on the shift properties. When compared with existing fast algorithms, the proposed approaches are more efficient in terms of computational burden, and also provide arbitrary choice of transform length