State-space representations of 2-D FIR lossless matrices and their application to the design of 2-D subband coders

The authors provide a general characterization of p×p lossless 2-D FIR (finite impulse response) transfer matrices of arbitrary degree in (z₁, z ₂). The properties of 2-D state-space realizations of such matrices are examined. It is shown that these matrices are not necessarily decomposable of a product of 1-D matrix transfer functions depending on z₁ and z₂ separately. An approach to the design that does not exclude any lossless filter of a given degree is presented. An illustrative example which covers a subset of the ideas discussed is presented. This example consists of a two-band lossless filter bank suitable for hexagonal subsampling