The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processi...

In this paper, a new texture classification method is provided for dividing texture images into three classes: periodic, directional, and random. The method is based on the fact that for a directional texture image, the magnitudes of its Fourier spectrum will concentrate on a certain direction; for periodic, on several directions; and for random, spread out over all directions. To use this fact...

We derive exact analytical expressions for the spatial Fourier spectrum of soliton family on a constant background. Also known as breathers, these solitons are solutions nonlinear Schrödinger equation and considered prototypes rogue wave models. Depending periodicity in spatial-temporal domain, characteristics wavenumber-temporal domain may feature either continuous or discrete spectrum.