Biorthonormal filter banks: some necessary conditions, and orthonormalization

Some properties of nonuniform biorthonormal filter banks are studied. It is shown that biorthonormality imposes a number of restrictions on the decimation ratios, e.g., they cannot be relatively prime. Biorthonormality implies orthonormality when all the impulse responses have the same energy. After a brief study of these properties, it is shown how to orthonormalize a nonuniform biorthonormal system by a procedure that is somewhat similar in spirit to (but fundamentally different from) the Gram Schmidt procedure. The procedure is modified for the purpose of designing biorthonormal filter banks that completely decorrelate the subband signals for given input statistics