Optimal two channel synthesis IIR filter banks with subband noise

We discuss the design of IIR synthesis filter banks with subband noise. Here we interpret filter banks (FB) as multiple input multiple output (MIMO) systems. The design of the FB is done obtaining the optimal IIR causal stable filter for a MIMO system in a mean squared error (MSE) sense. In this way, it is necessary to factorize a matrix whose entries are the estimations of the spectral densities of each subband signal. For the two bands case, if the diagonal entries of the matrix are all poles rational functions, the factorization can be obtained.