In this paper we solve an open problem concerning the characterization of those measurable sets $\Omega\subset \mathbb{R}^{2d}$ that, among all having a prescribed Lebesgue measure, can trap largest possible energy fraction in time-frequency space, where density generic function $f\in L^2(\mathbb{R}^d)$ is defined terms its Short-time Fourier transform (STFT) $\mathcal{V} f(x,\omega)$, with Gau...

Induction motors are a critical component of many industrial processes and are frequently integrated in commercially available equipment and industrial processes. The studies of induction motor behavior during abnormal conditions, and the possibility to diagnose different types of faults have been a challenging topic for many electrical machine researchers. The Motor Current Signature Analysis ...

This paper is devoted to some problems that appear in derivations of the discrete time Fourier transform from a formula for its continuous counterpart transformation into frequency domain as well those regarding inverse direction. In particular, latter ones remained so far an unresolved problem. It solved first here. Many detailed explanations accompanying solution found are presented. Finally,...

A new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a fractional domain. It exploits the combined advantages of WT and fractional Fourier transform (FrFT). The transform permits the identification of a tran...