Minimax passband group delay nonlinear fir filter design without imposing desired phase response

In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed magnitude square response over both the passband and the stopband. This filter design problem is a nonsmooth functional inequality constrained optimization problem. To tackle this problem, first, the one norm functional inequality constraint of the optimization problem is approximated by a smooth function so that the nonsmooth functional inequality constrained optimization problem is approximated as a noncon-vex functional inequality constrained optimization problem. Then, a modified filled function method is applied for finding the global minimum of the nonconvex optimization problem. Computer numerical simulation results show that our designed nonlinear phase peak constrained FIR filter could achieve lower minimum passband group delay than those of existing designs.