Design of sparse constrained FIR filter using orthogonal matching pursuit method

In this paper, the design of sparse constrained linear phase FIR filter is investigated. First, the design problem of sparse constrained FIR filter is described. Then, the orthogonal matching pursuit (OMP) method is presented to design sparse constrained FIR filter. Next, two kinds of filters are studied. One is the sparse FIR notch filter with controlled null width, the other is the sparse low-pass filter with derivative constraints. Finally, some numerical examples are demonstrated to show the effectiveness of the proposed design methods.