Multiple features can be extracted from time-frequency representation of signals for the purpose acoustic event detection. However, many underwater are formed by multiple events (impulsive and tonal), which generates difficulty on high-resolution TFR each component. For characterization such different events, we propose an anisotropic chirplet transform to achieve with high energy concentration...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

Analysis and extraction of strongly frequency modulated signals have been a challenging problem for adaptive data analysis methods, e.g., empirical mode decomposition [N.E. Huang et al., R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 454 (1998), pp. 903–995]. In fact, many of the Newtonian dynamical systems, including conservative mechanical systems, are sources of signals with low to strong...

We give a representation theorem for Hilbert algebras by means of ordered sets and characterize the homomorphisms of Hilbert algebras in terms of applications defined between the sets of all irreducible deductive systems of the associated algebras. For this purpose we introduce the notion of order-ideal in a Hilbert algebra and we prove a separation theorem. We also define the concept of semi-h...

For the analysis of time series data from hydrology, we employ a technique recently developed in Huang et al., 1998, which is by now widely known as the Hilbert-Huang-Transform (HHT). Specifically, it is designed for nonlinear and nonstationary data. In contrast to data analysis techniques employing the short-time/windowed Fourier transform or the continuous wavelet transform, the new technique...

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some approximations for the n-time di¤erentiable functions of selfadjoint operators in Hilbert spaces by two point Taylor’s type expansions are given. 1. Introduction Let U be a selfadjoint operator on the complex Hilbert space (H; h:; :i) with the spectrum Sp (U) included in the interval [m;M ] for some real n...