Wavelet transformation is one of the most practical mathematical transformations in the field of image processing, especially image and signal processing. Depending on the nature of the multiresolution analysis, Wavelet transformation become more accessible and powerful tools. In this paper, we refer to the mathematical foundations of this transformation.   Introduction: The...

In this paper we present a new method of signal processing for robust speech recognition using multiple microphones. The method, based on human binaural hearing, consists of passing the speech signals detected by multiple microphones through bandpass filtering and nonlinear rectification operations, and then cross-correlating the outputs from each channel within each frequency band. These opera...

Low-rank approximations play an important role in systems theory and signal processing. The problems of model reduction and system identification can be posed and solved as a low-rank approximation problem for structured matrices. On the other hand, signal source separation, nonlinear system identification, and multidimensional signal processing and data analysis can be approached with powerful...

A nonlinear electrical transmission line with an intersite circuit element acting as a nonlinear resistance is introduced and investigated. In the continuum limit, the dynamics of localized signals is described by a nonlinear evolution equation belonging to the family of nonlinear diffusive Burgers’ equations. This equation admits compact pulse solutions and shares some symmetry properties with...

Hilbert Huang Transform (HHT) is an empirical timefrequency analysis method firstly proposed by N. E. Huang in 1998. This method is suitable for nonlinear and non-stationary signal processing and thus employed for bioelectrical signal processing and analysis in recent years. However, the large computation cost of HHT restricts its applications for real-time signal processing. This paper present...

The novel approach was developed for multilevel signal detection in channels with impulsive nonGaussian noise. This approach consists of using morphological nonlinear image filtration principles for two dimensional signals. It is a new method of signal demodulation, using three dimensional image processing algorithms. Successful results of this morphologic detector encourage more investigation ...

Graphons are infinite-dimensional objects that represent the limit of convergent sequences graphs as their number nodes goes to infinity. This paper derives a theory graphon signal processing centered on notions Fourier transform and linear shift invariant filters, counterparts graph filters. It is shown for associated signals: (i) converges when bandlimited; (ii) spectral vertex responses filt...