Real-time determination of IIR coefficients for cascaded Butterworth filters

Beginning with an s-domain description of the basic second-order RCL filter network, the digital filter equivalent is derived using the bilinear transformation. The resulting formulas describing the z-domain digital response are algebraically reduced to a form that gives some intuitive insight into the fundamental symmetry relationships between analog and digital filter structures. A simplified description of the digital filter coefficients whose form lends itself to real-time computational techniques is presented. This analysis is extended to the cascaded second-order network characterized by Butterworth damping factors, so that higher order filters can be designed and implemented in real-time using high-speed digital signal processors such as the DSP 56001 and DSP 96002