An LMI approach to the design of 2D FIR multirate filter banks

In this paper, we consider the design of 2D (two-dimensional) FIR (finite impulse response) multirate filter banks. For a given 2D FIR analysis filter bank, we design a 2D FIR synthesis filter bank to minimize the reconstruction error of the filter banks such that the worst case energy gain between the input and the reconstruction error is below a prescribed bound. Our solution is formulated in terms of a set of linear matrix inequalities (LMIs) which can be directly computed by Matlab.