CLASSIFICATION OF NONEXPANSIVE SYMMETRICAL EXTENSION TRANSFORMS FOR MULTIRATE FILTER BANKS

This paper describes and classifies a family of invertible discrete-ti me signal transforms, referred to as symmetric extension trans forms ( SET's), for finite-length signals. SET's are algorithms for applying p erfect reconstruction multirate filter banks to symmetric extensions o f finite-length signals, thereby avoiding the boundary artifacts intro duced by simple periodic extension. A key point is when such symmetric decompositions can be formed with no increase in data storage require ments (''nonexpansive decompositions''). Transforms based on three typ es of symmetric extension and four classes of linear phase filters are analyzed in terms of their memory requirements for general M-channel perfect reconstruction filter banks. The classification is shown to be complete in the sense that it contains all possible nonexpansive SET' s. Completeness is then used to deduce design constraints on the const ruction of nonexpansive M-channel SET's, including new obstructions to the existence of certain classes of filter banks. This paper also for ms the principal technical reference on the SET algorithms incorporate d in the Federal Bureau of Investigation's digital fingerprint image c oding standard.