Biorthonormal filter banks: some necessary conditions, and orthonormalization

We first study some properties of nonuniform biorthonormal filter banks. We show that biorthonormality imposes a number of restrictions on the decimation ratios, e.g., they cannot be relatively prime. Also biorthonormality implies orthonormality when all the impulse responses have the same energy. After a brief study of these properties we show 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. We then modify the procedure for the purpose of designing biort honormal filter banks that completely decorrelate the subband signals for a given input statistics.