Optical half-band filters

This paper proposes two kinds of novel 2 x 2 circuit configuration for finite-impulse response (FIR) half-band filters, These configurations can be transformed into each other hy a symmetric transformation and their power transmittance is identical, The configurations have only about half the elements of conventional FIR lattice-form filters. We derive a design algorithm for achieving desired power transmittance spectra, We also describe 2 x 2 circuit configurations for infinite-impulse response (IIR) half-band filters. These configurations are designed to realize arbitrary-order IIR half-band filter characteristics by extending the conventional half-band circuit configuration used in millimeter-wave devices. We discuss their filter characteristics and confirm that they have a power half-band property. We demonstrate design examples including FIR maximally flat half-band filters, an FIR Chebyshev half-band filter, and an IIR elliptic half-band filter.