Linear transforms and filterbanks based on vector ARMA models

Abstract

Linear transformations, like wavelet transforms, and filterbanks of IIR-type and of arbitrary time-frequency plane tilings can be efficiently realized by vector ARMA models. The quality of the realization depends on how well the basis functions or impulse responses of the filterbank can be approximated by the actual VARMA based pole-zero model. The vector AR part gives an MSE-optimal block-recursive model for the target basis functions. The vector MA part is formed of the vector AR residual and further optimized by an iterative algorithm.