The Fourier transform remains one of the most popular spectral methods in time-series analysis, so much so that the word “spectrum” is virtually equivalent to “Fourier spectrum” (Huang et al., 2001). This method assumes that a time series extends from positive to negative infinity (stationarity) and consists of a linear superposition of sinusoids (linearity). However, geophysical signals are ne...

The Fourier transform remains one of the most popular spectral methods in time-series analysis, so much so that the word “spectrum” is virtually equivalent to “Fourier spectrum” (Huang et al., 2001). This method assumes that a time series extends from positive to negative infinity (stationarity) and consists of a linear superposition of sinusoids (linearity). However, geophysical signals are ne...

this paper is concerned with a technique for solving volterra integral equations in the reproducing kernel hilbert space. in contrast with the conventional reproducing kernel method, the gram-schmidt process is omitted here and satisfactory results are obtained.the analytical solution is represented in the form of series.an iterative method is given to obtain the approximate solution.the conver...

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides no...

Ground state of the dissipative two-state system is investigated by means of the Lanczos diagonalization method. We adopted the Hilbert-space-reduction scheme proposed by Zhang, Jeckelmann and White so as to reduce the overwhelming reservoir Hilbert space to being tractable in computers. Both the implementation of the algorithm and the precision applied for the present system are reported in de...

Estimation of the modal parameters of mechanical systems or structures is usually achieved by applying the well-known Frequency Response Function (FRF) method to experimental data obtained from free vibration after a shock excitation of the system or forced vibration using a variety of excitation signals. This method is however limited only to linear systems. The problem becomes more complex wh...