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Good initial values are crucial to obtain solutions of nonconvex optimization problems. When estimating the transfer function of physical systems from measured noisy data, obtaining good initial parameter estimates is therefore a primordial step. In this paper, it is shown that smoothing the measured frequency response function of a linear time-invariant system enhances the construction of initial estimates significantly, resulting in the optimization schemes to converge to a better optimum. This is achieved with minimal user interaction. Two smoothing techniques, the time-truncated local polynomial method and the regularized finite impulse response, are compared with the existing generalized total least squares and the bootstrapped total least squares initial estimates. The improvement attributable to smoothing is demonstrated by a simulation and by measurements of an electrical filter. The results ultimately show that the parametric models obtained using the proposed starting values are much more likely to give a good description of the measured system and hence lead to more useful models. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

The logarithmic distribution of spectral lines in excitation signals is widely used to measure the transfer functions of dynamic systems over a wide frequency band, covering several decades. Periodic signals are very popular in many advanced dynamic signal analyzers. Generating multitone periodic signals requires an equidistant frequency grid which conflicts with the logarithmic distribution, particularly at the low frequencies. In this paper, we offer an elegant solution to get around this problem using an improved choice for the amplitude spectrum of the multitone. We also offer a simple way to tune the frequency spacing of such a signal to allow for robust identification of the system under test. [ABSTRACT FROM AUTHOR]