A Second-Order Lowpass Parameter-Varying Filter Based on the Interconnection of First-Order Stages

In recent years, a new class of filters known as parameter-varying filters has been proposed. These filters are characterized by having a transient response of reduced duration while preserving their frequency response properties. The reduction of the transient response of these filters is a consequence of the automatic adjustment of their parameters. These filters may be used in signal processing applications in which the influence of the transient behavior of the filter is seen as an unwanted component of the filter output. In this article, a second-order lowpass parameter-varying filter based on the cascade of first-order parameter-varying stages is presented. The stability properties of the proposed filter, and particularly its bounded-input, bounded-output stability, are verified using a linear time-varying model which accurately represents its behavior when it is subject to the variation of its parameters. The parameters of the filter are varied according to a predefined control strategy. Simulation results confirm the filter capabilities to shorten the duration of its transient behavior when its parameters are varied through the action of a nonlinear control loop.