Constrained least-squares design and characterization of affine phase complex FIR filters

In many signal processing applications, the need arises for the design of complex coefficient finite impulse response (FIR) filters to meet the specifications which cannot be approximated by real coefficient FIR filters. The paper presents a new technique for the design of complex FIR filters based on minimizing a weighted integral squared-error criterion subject to the constraint that the resulting filter response be affine phase (i.e., generalize linear phase), The technique makes use of the necessary and sufficient conditions for a causal complex FIR filter to possess affine phase which are explicitly derived in the present paper. The method is non-iterative and computationally efficient. Several illustrative filter design examples are presented with excellent results