Optimal all-pole filter design based on discrete prolate spheroidal sequences

A new constrained optimization method for all-pole digital filter design is presented. The design philosophy employed minimizes a function of the area between the ideal low-pass filter response in the passband and the actual filter response subject to a quadratic constraint which ensures filter realizability. It is shown that unique solutions are obtained which are related to eigenvectors of a Toeplitz matrix whose elements form a scaled discrete prolate spheroidal wave sequence (DPSS). It is therefore possible to exploit the properties of DPSS and discrete prolate spheroidal wave functions (DPSWF´s) to reduce the filter design effort. The ratio of passband energy to total energy over the entire filter bandwidth is optimal for these designs.