Magnitude response peak detection and control using balanced model reduction and leakage to a target

Adaptive filters are often used in systems that need to adjust to unknown environments. Communication channels with frequency nulls, signals that lack energy in a frequency band, and transducers with a finite bandwidth present special problems since adaptive filters can develop a large gain at frequencies where excitation is lacking. Such magnitude response peaks can cause problems if unchecked. This paper suggests a procedure for detecting and controlling magnitude response peaks that uses a balanced model reduction technique to form a low-order IIR filter that approximates the performance of the filter. The poles are then studied to determine if magnitude response peaks are present. If a peak is detected, then “leakage to a target” is used to gradually reduce the peak with minimal effect on the equalizer´s response at other frequencies. Several useful bounds on the equalizer frequency response magnitude are derived, and the frequency domain behavior of the leakage to a target algorithm is analyzed. A case study is provided