Time-varying lapped transforms and wavelet packets

The perfect reconstruction conditions for a time-varying lapped transform (paraunitary filter bank) are developed through the factorization of the transform matrix into sparse factors. A general formulation is presented allowing one to switch between two paraunitary filter banks. However, the extended lapped transform (ELT) is often used as an example. Furthermore, an adaptive wavelet packet is developed employing a time varying, tree association of ELTs. In all cases perfect reconstruction is inherently assured.>