This work investigates how stochastic unmeasurable sampling jitter noise affects the result of system identification, and proposes a modification of known approaches to mitigate the effects of sampling jitter. By just assuming conventional additive measurement noise, the analysis shows that the identified model will get a bias in the transfer function amplitude that increases for higher frequencies. A frequency domain approach with a continuous time system model allows an analysis framework for sampling jitter noise. The bias and covariance in the frequency domain model are derived. This is used in bias compensated (weighted) least squares algorithms, and by asymptotic arguments this leads to a maximum likelihood algorithm. Continuous time output error models are used for numerical illustrations.Keywords: system identification, stochastic systems, least-squares estimation, maximum likelihood, frequency domain Identification with Stochastic Sampling Time Jitter ⋆ Frida Eng1 , Fredrik Gustafsson. Dept of EE, Linköpings universitet, SE-58183 Linköping, Sweden AbstractThis work investigates how stochastic unmeasureable sampling jitter noise affects the result of system identification, and proposes a modification of known approaches to mitigate the effects of sampling jitter. By just assuming conventional additive measurement noise, the analysis shows that the identified model will get a bias in the transfer function amplitude that increases for higher frequencies. A frequency domain approach with a continuous time system model allows an analysis framework for sampling jitter noise. The bias and covariance in the frequency domain model are derived. This is used in bias compensated (weighted) least squares algorithms, and by asymptotic arguments this leads to a maximum likelihood algorithm. Continuous time output error models are used for numerical illustrations.

In non-uniform sampling (NUS), signal amplitudes and time stamps are delivered in pairs. Several methods to compute an approximate Fourier transform (AFT) have appeared in literature, and their posterior properties in terms of alias suppression and leakage have been addressed. In this paper, the sampling times are assumed to be generated by a stochastic process. The main result gives the prior distribution of several AFTs expressed in terms of the true Fourier transform and variants of the characteristic function of the sampling time distribution. The result extends leakage and alias suppression with bias and variance terms due to NUS. Specific sampling processes as described in literature are analyzed in detail. The results are illustrated on simulated signals, with particular focus to the implications for spectral estimation. In non-uniform sampling (NUS), signal amplitudes and time stamps are delivered in pairs. Several methods to compute an approximate Fourier transform (AFT) have appeared in literature, and their posterior properties in terms of alias suppression and leakage have been addressed. In this paper, the sampling times are assumed to be generated by a stochastic process. The main result gives the prior distribution of several AFTs expressed in terms of the true Fourier transform and variants of the characteristic function of the sampling time distribution. The result extends leakage and alias suppression with bias and variance terms due to NUS. Specific sampling processes as described in literature are analyzed in detail. The results are illustrated on simulated signals, with particular focus to the implications for spectral estimation.

Decimating a uniformly sampled signal a factor D involves low-pass antialias filtering with normalized cutoff frequency 1/D followed by picking out every Dth sample. Alternatively, decimation can be done in the frequency domain using the fast Fourier transform (FFT) algorithm, after zero-padding the signal and truncating the FFT. We outline three approaches to decimate nonuniformly sampled signals, which are all based on interpolation. The interpolation is done in different domains, and the intersample behavior does not need to be known. The first one interpolates the signal to a uniformly sampling, after which standard decimation can be applied. The second one interpolates a continuous-time convolution integral, that implements the antialias filter, after which every Dth sample can be picked out. The third frequency domain approach computes an approximate Fourier transform, after which truncation and IFFT give the desired result. Simulations indicate that the second approach is particularly useful. A thorough analysis is therefore performed for this case, using the assumption that the non-uniformly distributed sampling instants are generated by a stochastic process.

When the sensors readings are perturbed by an unknown stochastic time jitter, classical system identification algorithms based on additive amplitude perturbations will give biased estimates. We here outline the maximum likelihood procedure, for the case of both time and amplitude noise, in the frequency domain, based on the measurement DFT. The method directly applies to output error continuous time models, while a simple sinusoid in noise example is used to illustrate the bias removal of the proposed method. Abstract When the sensors readings are perturbed by an unknown stochastic time jitter, classical system identification algorithms based on additive amplitude perturbations will give biased estimates. We here outline the maximum likelihood procedure, for the case of both time and amplitude noise, in the frequency domain, based on the measurement DFT. The method directly applies to output error continuous time models, while a simple sinusoid in noise example is used to illustrate the bias removal of the proposed method.

This work investigates how stochastic unmeasureable sampling jitter noise affects the result of system identification, and proposes a modification of known approaches to mitigate the effects of sampling jitter. By just assuming conventional additive measurement noise, the analysis shows that the identified model will get a bias in the transfer function amplitude that increases for higher frequencies. A frequency domain approach with a continuous time system model allows an analysis framework for sampling jitter noise. This leads to a bias compensated (weighted) least squares algorithm. A continuous time output error model is used for numerical illustration.