Correspondence: [email protected] Nalecz Institute of Biocybernetics and Biomedical Engineering PAS, Warsaw, Poland Abstract Background: In analysis of nonstationary nonlinear signals the classical notion of frequency is meaningless. Instead one may use Instantaneous Frequency (IF) that can be interpreted as the frequency of a sine wave which locally fits the signal. IF is meaningful for mon...

We propose a learning algorithm for selforganizing neural networks to form a topology preserving map from an input manifold whose topology may dynamically change. Experimental results show that the network using the proposed algorithm can rapidly adjust itself to represent the topology of nonstationary input distributions. key words: competitive Hebbian learning rule, law of the jungle mechanis...

An idea for how to reconstruct the quantum state of a nonstationary single-photon wave packet absorbed in a macroscopic medium with inhomogeneously broadened lines is presented. An analytical treatment of the problem is performed and the requirements on the proposed scheme for complete recovery of the recorded nonstationary quantum state with a probability close to unity is described. The physi...

Nonstationary Gabor frames were recently introduced in [2] and represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. In this paper we show a general existence result for this family of frames. We also construct nonstationary Gabor frames with non-compactly supported windows from a related painless nonorthogona...

We address the problem of structural model identification during normal operating conditions and thus with uncontrolled, unmeasured, and nonstationary excitation. We advocate the use of output-only and covariance-driven subspace-based stochastic identification methods. We explain how to handle nonsimultaneously measured data from multiple sensor setups, and how robustness with respect to nonsta...

Frequency domain statistics are studied in the presence of fractional deterministic and stochastic trends. It is shown how the behaviour of the sample variance-covariance matrix of nonstationary processes can be dominated by components corresponding to a possibly degenerating band around zero frequency. This property is used to establish the limiting distribution of the averaged periodogram mat...

We incorporate the use of validation data to cope with noisy records in a neural network-based method for modelling the dynamics of slowly-changing nonstationary systems. As a byproduct, we obtain a precise criterion to find the optimal value of a required internal hyperparameter. Testing these ideas on a controlled problem shows that the resulting algorithm is able to outperform previous metho...

Asymptotic inference on nonstationary fractional time series models, including cointegrated ones, is proceeding along two routes, determined by alternative definitions of nonstationary processes. We derive bounds for the mean squared error of the difference between (possibly tapered) discrete Fourier transforms under the two regimes. We apply the results to deduce limit theory for estimates of ...