J. Schoukens

Parametric identification of transfer functions in the frequency domain-a survey

This paper gives a survey of frequency domain identification methods for rational transfer functions in the Laplace (s) or z-domain. The interrelations between the different approaches are highlighted through a study of the (equivalent) cost functions. The properties of the various estimators are discussed and illustrated by several examples. >

The interpolated fast Fourier transform: a comparative study

The properties of five interpolating fast Fourier transform methods (IFFT) are studied with respect to their systematic errors and their noise sensitivity, for a monofrequency signal. It is shown that windows with small spectral sidelobes do not always result in a better overall performance of the IFFT and that time-domain estimators can be more efficient than the IFFT methods analyzed. It is also, shown that time-domain techniques have a lower Cramer-Rao lower bound than the IFFT methods, which can result in more efficient estimates. >

Peak factor minimization using a time-frequency domain swapping algorithm

An algorithm is presented to minimize the peaks in the time domain of bandlimited Fourier signals. This method has the ability to compress signals effectively without disturbing their spectral magnitudes. A computationally efficient algorithm is presented that leads to strongly compressed signals (crestfactors of 1.41 compared to 1.67). The method is applicable not only to flat spectrum magnitudes but to any frequency domain energetic distribution. >

Frequency domain system identification using arbitrary signals

It is the common conviction that frequency domain system identification suffers from the drawback that it cannot handle arbitrary signals without introducing systematic errors. This paper shows that it is possible to deal with nonperiodic signals without any approximation and under the same assumptions as in the time domain, by estimating simultaneously some initial conditions and the system model parameters.

Modeling the noise influence on the Fourier coefficients after a discrete Fourier transform

An analysis is made to study the influence of time-domain noise on the results of a discrete Fourier transform (DFT). It is proven that the resulting frequency-domain noise can be modeled using a Gaussian distribution with a covariance matrix which is nearly diagonal, imposing very weak assumptions on the noise in the time domain.

Survey of excitation signals for FFT based signal analyzers

The properties of ten different excitation signals are studied to analyze their suitability as excitation signals for fast Fourier transform (FFT)-based signal and network analyzers. Their influence on the measurement time, accuracy, and sensitivity to nonlinear distortions is described. The flexibility to create a customized amplitude spectrum is investigated. With this information it becomes possible to select the best excitation signal for many applications. >

Peak factor minimization of input and output signals of linear systems

An overview is given of existing analytical and numerical methods for the comparison of the peaks of discrete, finite sum of sines. A novel method that compresses the signals optimally or almost optimally is presented. The algorithm is extended to the simultaneous compression of the input and output signals of a linear system. The implications of strong signal compression for the signal-to-noise ratio lead to the formulation of a two-step optimal experimental setup for system identification and parameter estimation of linear systems. >

Identification of linear dynamic systems using piecewise constant excitations: use, misuse and alternatives

Abstract Time domain identification of linear dynamic systems using discrete time models relies heavily on the use of piecewise constant excitation signals (ZOH-assumption). If this assumption is not met, severe errors can be generated and the results can be useless. In this article we study the implications of the ZOH-assumption and an alternative is formulated. This leads to frequency domain identification methods based on the band limited assumption (that the signals obey the Shannon sampling theory). The theory and practical aspects of both approaches are compared. Finally, it will be shown that periodic excitations (or perturbation signals) can offer significant advantages in both approaches.

Robust identification of transfer functions in the s- and z-domains

A frequency-domain maximum-likelihood estimator (MLE) for estimating the transfer function of linear continuous-time systems developed by J. Schoukens et al. (1988) assumes independent Gaussian noise on both the input and the output coefficients. A Gaussian frequency-domain MLE for transfer functions of linear continuous or discrete time invariant systems in an errors-in-variables model is presented. It is demonstrated that most of the properties of the estimator remain unchanged when it is applied to measured input and output Fourier coefficients corrupted with non-Gaussian errors. The result is a robust Gaussian frequency-domain estimator that is very useful for the practical identification of linear systems. The theoretical results are verified by simulations and experiments. >

A maximum likelihood estimator for linear and nonlinear systems-a practical application of estimation techniques in measurement problems

A method is presented for estimating the parameters of linear systems and nonlinear systems. The linear systems are modeled by their transfer function, while the nonlinear systems are described by a Volterra series. The estimator belongs to the class of maximum-likelihood estimators. During the estimation process, the Cramer-Rao lower bound on the covariance matrix of the estimates is derived. >