Design and analysis of matrix Wiener synthesis filter for multirate filter bank

In this paper, we present a solution to the problem of reconstructing the input of a maximally decimated filter bank from the subband components using Wiener filtering. We present a generalized structure for applying Wiener filtering at the output of the analysis stage of a uniform filter bank (UFB). This structure can be used to model a situation where the desired signal is a filtered version of the input signal. Some interesting results for matrix inversion are derived and used to reduce the complexity of the Wiener filter expression. The resulting expression provides many insights into the properties of the Wiener synthesis filter designed. The Wiener synthesis filter turns out to be independent of the input spectral properties. The proposed Wiener synthesis filter bank exploits the pseudocirculant property. Thus all distortions are completely removed and the filter bank reduces to a linear time invariant (LTI) filter of interest. We later extend the analysis to non-uniform filter banks (NUFBs).