Quantifying Adaptive Performance Improvement in the Frequency Domain

A new input/output analysis technique is introduced to rigorously describe adaptive system performance in a frequency domain sense. Signals are decomposed onto orthogonal subspaces, representing individual frequency components, and spectral bounds for the prediction error are derived. The problem formulation compares adaptive system performance relative to a fixed, nominal system, providing a direct measure of the performance benefits of adaptation. Simulation of an adaptive identification algorithm is used to indicate the accuracy of the analysis method, showing that the subspace approach can provide substantially improved measures of algorithm performance.