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A structure is presented for implementing perfectly reconstructing time-varying linear-phase paraunitary filterbanks (LPPUFB) using a novel adaptive lapped transform (ALT). The ALT is based on the generalized lapped orthogonal transform (GenLOT). A time-varying filterbank is constructed through the factorization of the GenLOT into cascaded matrix stages. Variable-length lapped transforms are subsequently generated by cascading a number of these matrix stages to build filters of specific length. An embedded ALT image codec is presented.