An Alternative Minimax Design of Sparse IIR Filters Based on L1-Norm

In this paper, we propose an alternative design of a class of sparse IIR filters in the minimax sense. By utilizing the L1-norm to achieve the coefficient sparsity and iteratively updating the denominator of the transfer function, we transform the design problem to a second-order cone. The proposed design is then accomplished in two phases. The locations of zero coefficients of the filter numerator are identified in the first phase by using a convex program solver. In the second phase, the filter with sparse numerator coefficients is re-optimized in the minimax sense subject to an easy-to-use stability constraint. Numerical examples are given to show the effectiveness of the proposed method.