Adaptive bilinear digital filters

How adaptive algorithms can be applied to low-sensitivity digital filter structures is shown. The considered structure is derived by a bilinear transformation of an analog doubly resistively terminated ladder filter. A fifth-order IIR low-pass filter is used as example. The adaptive algorithm is derived using standard stochastic approximation arguments and both gradient and Newton updating equations are presented. The adaptive bilinear filter is used in system identification simulations and compared to a direct-form IIR filter. It is demonstrated that the adaptive bilinear filter, although not unconditionally stable, has excellent stability properties. It is also shown that the adaptive algorithm can be used as a tool for synthesis of pseudopassive and hence numerically robust fixed filters. The adaptive algorithm is used to minimize a cost function chosen as a weighted difference between the desired transfer function and the adaptive transfer function