Characterization of a set of invertible LPTV filters using circulant matrices

Abstract

We propose a class of invertible linear periodically time varying (LPTV) filters. After introducing modulator and MIMO representations of LPTV filters, we associate a matrix formulation for these two representations. The inversion problem is then studied leading to a matrix inversion problem. Under a condition on the LPTV construction, the LPTV modulator matrix becomes circulant. Using the diagonalization properties of circulant matrices, the problem of inverting the N periodic LPTV filter reduces to the inversion of N linear time invariant (LTI) filters. An analytic expression of the LPTV inverse filter is given. Such invertible LPTV filters define a general set of LPTV filters in which, for example, convolutional interleavers are included. To illustrate the good LPTV properties of this class of LPTV filters, simulation results emphasize the spreading efficiency of this class.