Smoothing the LPM Estimate of the Frequency Response Function Via an Impulse Response Truncation Technique

A statistical impulse response truncation technique is applied to the local polynomial method (LPM)-estimate of the frequency response function (FRF), resulting in an improved, smooth FRF. Formulated as a nonparametric linear-least-squares-estimate, the LPM is first applied to estimate the FRF from a full data record of a single-input-single-output system, systematically expressed in an output-error framework. The smooth characteristics of both the exact FRF and the leakage from transients allow for an optimal application of the local polynomial method, leading to the elimination of both the leakage and interpolation errors. The truncation method introduced in this paper makes it possible for the user to fine-tune the tradeoff between the uncertainty (variance) and the bias on the estimated instantaneous FRF.