Designs of Chebyshev-type complex FIR filters and digital beamformers with linear-phase characteristics

Based on the theory of optimal polynomial approximation, the authors present a complex alternation theorem which shows the existence of Chebyshev complex FIR filters. According to the theorem, a method for designing Chebyshev-type complex FIR filter and DBFs with linear-phase characteristics is proposed. A zero exchange algorithm and the related procedures are used to iteratively find the best approximation to a variety of desired frequency responses and directivity patterns. Several examples are included to show the efficacy of the designs of FIR filters with multistop-/multipassband responses, DBFs with pencil beams and local low sidelobes, and pattern synthesis with a shaped mainlobe