Circularly symmetric filter design using 2D prolate spheroidal sequences

A new design method for 2D circularly symmetric FIR filters is presented which is based upon the constrained optimisation of the passband volume of the filters magnitude squared function. It is shown that if a quadratic constraint is employed the resulting filter coefficients are related to a set of 2D prolate spheroidal sequences. These filters have the property of concentrating the maximum energy into the filter passband and have a phase characteristic which is linear. The paper also extends the theory of discrete prolate spheroidal sequences to two dimensions.