Multidimensional filter banks and wavelets - a system theoretic perspective

The status of multidimensional filter banks and wavelets are reviewed from the perspective of circuits and systems theory. A degree of synergy between the two fields of wavelets and multidimensional systems arises from the fact that many ideas crucial to the wavelet design are inherently system theoretic in nature. The construction of orthogonal wavelets can be essentially viewed as a circuit and system theoretic problem of design of energy dissipative filters, the multidimensional version of which has very close ties with classic problem of lumped-distributed passive network synthesis. The problem of biorthogonal perfect reconstruction filterbank design can be viewed as a matrix completion problem in the ring of rational functions.