Comparison of the Balanced Truncation and Balanced Stochastic Truncation Algorithms in Model Order Reduction for IIR Digital Filters

In the field of system identification and modeling for dynamic systems, the increasing complexity and granularity of models often result in significantly higher computational costs and storage requirements, especially in real-time applications and optimization processes.To address this issue, model order reduction methods have been developed to produce reduced-order models with smaller dimensions while preserving the key dynamic characteristics of the original system.In this paper, two widely used model order reduction algorithms, Balanced Truncation (BT) and Balanced Stochastic Truncation (BST), are applied to reduce the order of high-order Infinite Impulse Response (IIR) digital filters.Analysis results reveal that BT outperforms BST in preserving the time-domain response and signal energy, whereas BST demonstrates superior performance in maintaining frequency-domain responses across the entire frequency range and preserving minimum-phase characteristics.Through comparisons of the reduction errors in terms of H and H-norms, the paper identifies that reducing the order from 30 to 11 and 15 achieves an optimal balance between accuracy and system complexity.These findings provide a basis for selecting appropriate algorithms in practical applications such as filter design, automatic control, and signal processing.