The Hilbert-Huang transform (HHT) is a powerful method for nonlinear and non-stationary vibrations analysis. This approach consists of two basic parts of empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). To achieve the reliable results, Bedrosian and Nuttall theorems should be satisfied. Otherwise, the phase and amplitude functions are mixed together and consequently, the ...

We investigate Nuttall-Pommerenke theorems for several variable homogeneous Pad~ approximants using ideas of Goncar, Karlsson and Wallin.

The analytic signal method via the Hilbert transform is a key tool in signal analysis and processing, especially in the time-frquency analysis. Imaging and other applications to multidimensional signals call for extension of the method to higher dimensions. We justify the usage of partial Hilbert transforms to define multidimensional analytic signals from both engineering and mathematical persp...

rticle history: vailable online xxxx eywords: iscrete Hilbert transform iscrete-time analytic signal edrosian product theorem The aim of this paper is to discuss discrete-time analytic signals and to provide the derivation of Bedrosian product theorem for discrete-time Hilbert transform. With the aid of the continuous-time analytic signals we provide a new approach to produce the discretetime a...

Analogues of the Nuttall-Pommerenke theorem and Wallin-type theorems for classical Pade approximants, are proved for linear and nonlinear Pade approximants formed from series of orthogonal polynomials, corresponding to a distribution da(x) with at most finitely many sign changes.