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.