Design of FIR filter using constrained L1 minimization method

In this paper, the design of digital FIR filter is investigated. First, filter design problem is described by considering various requirements except frequency response error. Then, the constrained L₁ minimization method in compressed sensing is applied to design FIR filter. As a result, dynamic range of filter coefficients, upper bound of filtering output, sparsity of filter coefficients, and error of frequency response can be controlled by suitably choosing the prescribed design parameter. Finally, some numerical comparisons with conventional least-squares design method are made to demonstrate the flexibility of this new design approach.