IIR filters with maximum impulse response symmetry

A class of optimum IIR discrete time systems based on the impulse response symmetry criterion is presented. Optimization of rational transfer function parameters of the second to the tenth order, with (i) zeros at the origin and (ii) zeros located on the real axis, is carried out. The optimum systems have the smallest symmetry error for a given system order. In the frequency domain they approximate a constant group delay and have a quasi Gaussian amplitude response. The filter design procedure is outlined. The impulse invariance method based on continuous time systems with symmetric impulse response is also considered.