Results on multidimensional nonuniform rational maximally-decimated filter banks with orthonormal filters

The framework of inner product space is introduced and used to derive some known and new filter bank results. It is shown that even the most general filter banks, namely, multidimensional nonuniform filter banks with rational decimation matrices, become a special case of this framework. The subband convolution scheme is obtained by starting from Parseval´s relation. Several theoretical wavelet transform results can be derived using this framework. In particular, the wavelet convolution theorem is derived.