COMPARISON AND EVALUATION OF THE MODAL TRUNCATION AND BALANCED TRUNCATION TECHNIQUES IN MODEL ORDER REDUCTION FOR IIR FILTERS

Abstract

This paper investigates model order reduction for a 30th-order IIR filter in telecommunication systems with the objectives of simplifying the structure, preserving dynamic characteristics, and reducing computational costs. Two algorithms, Modal Truncation and Balanced Truncation, are compared at reduced orders r = 13 and r = 15. At order 13, the H_∞ and H₂ errors for Balanced Truncation are 1.109873×10⁻² and 5.661614×10⁻³, respectively, which are lower than those for Modal Truncation, recorded at 2.097335×10⁻² and 1.805762×10⁻². Response analysis shows that with Balanced Truncation, after 30 seconds the time response of the reduced-order system closely follows that of the original system, and the frequency response above 10 rad/s also approximates that of the original system, whereas Modal Truncation consistently produces significant discrepancies. At order 15, the errors for Balanced Truncation further decrease (H∞: 1.233049×10⁻³, H₂: 8.219160×10⁻⁴) with the response nearly matching the original system, while Modal Truncation continues to exhibit substantial deviations. The results confirm that Balanced Truncation is a superior choice over Modal Truncation for model order reduction of IIR filters in telecommunication and signal processing applications.