Transient Time Reduction in Time-Varying Digital Filters via Second-Order Section Optimization

Time-varying digital filters are widely used in dynamic signal processing applications, but their transient response can significantly impact performance, particularly in real-time systems. This study focuses on reducing transient time in time-varying filters through second-order section (SOS) optimization. By employing a numerical optimization approach, we selectively adjust the coefficients of a single SOS within a higher-order filter to minimize the transient period while maintaining overall stability. Using a sequential quadratic programming (SQP) algorithm, we determine a time-varying coefficient trajectory over a finite horizon, ensuring a rapid convergence to steady-state behavior. Experimental results demonstrate that this targeted coefficient adaptation reduces transient time by up to 80% compared to conventional static designs, with minimal computational overhead. Additionally, a comparative analysis with traditional linear time-invariant (LTI) filters highlights the advantage of this method in suppressing transient oscillations while preserving long-term filter characteristics. The proposed approach provides a practical and efficient strategy for enhancing filter responsiveness in applications requiring both stability and real-time adaptability. These findings suggest that selective time variation in SOS decomposition can be a valuable tool in digital filter design, improving efficiency without excessive memory or processing demands.