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In analyzing non-stationary noisy signals with time-varying frequency content, it's convenient to use distribution methods in joint, time and frequency, domains. Besides different adaptive data-driven time-frequency (TF) representations, the approach with multiple orthogonal and optimally concentrated Hermite window functions is an effective solution to achieve a good trade-off between low variance and minimized stable bias estimates. In this paper, we propose a novel spectrogram method with multiple optimally parameterized Hermite window functions, with parameterization which includes a pair of free parameters to regulate the shape of the window functions. The computation is performed in the optimization process to minimize the variable projection (VP) functional problem. The proposed parametrized distribution method improves TF concentration and instantaneous frequency (IF) estimation accuracy, as shown in experimental results for synthetic signals and real-life ship motion response signals. With the optimization of nonlinear least-squares approximation of the ship response signals, the Hermite spectra are centralized, and only up to 15 basis functions are sufficient for concentration improvement in the TF domain. • Multiple Window Spectrogram method with parameterized Hermite functions is proposed. • The improved concentration representations were produced with two free parameters. • Several optimization methods with and without gradient information are implemented. • To avoid discontinuities in signal representations, we design nonlinear constraints. • The proposed method leads to improved time-frequency representation in ship systems. [ABSTRACT FROM AUTHOR]

Abstract: Performance and simulation-based optimization of the improved intersection of confidence intervals (ICI) rule for adaptive filter support selection are presented. The improved ICI rule (refereed to as the relative intersection of confidence intervals (RICI) rule) is combined with the local polynomial approximation (LPA) method and applied to signal denoising, with the aim to enhance the signal estimation accuracy and reduce the estimation error energy. The results achieved using the RICI rule are compared to those obtained using the classical ICI rule, showing the reduction of the root mean-square error (RMSE) of up to 10 times for various classes of analyzed signals. The proposed procedure for the selection of the RICI parameters Γ and , for which the RMSE is minimum, has been shown to significantly improve the quality of denoised signals. [Copyright &y& Elsevier]