Minimax design of quadrature mirror filters with prescribed stopband characteristics

In this paper, we present a novel approach for the minimax design of the quadrature mirror filters (QMF) with prescribed stopband characteristics. The advantage of this new approach is that the shape of the stopband response of the designed QMF can be arbitrarily controlled while the reconstruction error is optimally minimized in the minimax sense. Although the considered design problem is originally found to be a nonlinearly constrained optimization problem, it is shown that this problem can be solved efficiently by only solving a sequence of linear equation sets. The effectiveness of the proposed technique is shown by computer simulation examples.