A novel algorithm for the design of selective FIR filters with arbitrary amplitude and phase characteristics

In this paper, a novel analytic technique is presented for the design of finite impulse response digital filters with simultaneous amplitude and phase requirements. The design process relies on the interpolation concept and is based on the generation of arbitrary amplitude and phase polynomials. The new class of FIR filters lays in between the exact linear phase filters at all frequencies and the minimum phase FIR filters based on the amplitude approximation only. It interpolates arbitrary (e.g., linear) phase response in the passband and arbitrary amplitude characteristics in pass- and stopbands. The introduced class of filters can be used on the amplitude and phase equalization of both FIR and IIR digital filters. Illustrative examples are included in order to investigate the main properties of these filters and to demonstrate that the proposed design method leads to a significant saving in the arithmetic computations.