Design of bilinear digital ladder filters

Methods for designing bilinear switched-capacitor (SC) ladder filters are well known. However, they cannot be directly extended to digital filters because of the delay-free loops allowed in SC filters. In the present paper, design methods for low-sensitive bilinearly transformed voltage-current ladder filters are developed. The matrix approach for SC filter design is extended to digital filters, and the delay-free loops are eliminated. The design equations for general order lowpass, highpass, bandpass, bandstop, and allpass filters are obtained in a simple closed form. The design procedure gives a canonical number of delays and a number of distinct multipliers equal to the number of reactive elements in the prototype