The efficacy of anisotropic versus isotropic filtering is analyzed with respect to general phase-based metrics for early vision attributes. We verified that the spectral information content gathered through oriented frequency channels is characterized by high compactness and flexibility, since a wide range of visual attributes emerge from different hierarchical combinations of the same channels...

By applying a reflection principle we set up fully explicit representation formulas for the harmonic Green’s function for orthogonal sectors of the annulus of the unit ball of R. From the harmonic Green’s function we then can determine the Bergman kernel function of Clifford holomorphic functions by applying an appropriate vector differentiation. As a concrete application we give an explicit an...

The work presented in this paper aims to continue the progress obtained in the development of a ray tracing based simulation platform for realistic doubly selective radio channels. This framework is the integration of various propagation models present in literature, with a novel method to characterise the obstacles present in the radio path, relying only in point scatterers with specific chara...

We characterize precisely the possible rate of decay of the anti-analytic half of a trigonometric series converging to zero almost everywhere.

This paper introduces a two-dimensional (2-D) generalization of the analytic signal. This novel approach is based on the Riesz transform, which is used instead of the Hilbert transform. The combination of a 2-D signal with the Riesz transformed one yields a sophisticated 2-D analytic signal: the monogenic signal. The approach is derived analytically from irrotational and solenoidal vector field...

The discrete time–frequency matched filter should replicate the continuous time–frequency matched filter. But the methods differ. To avoid aliasing the discrete method transforms the real-valued signal to the complex-valued analytic signal. The theory for the time–frequency matched filter does not consider the discrete case using the analytic signal. We find that the performance of the matched ...

We challenge the perception that we live in a “proper world,” where complex random signals can always be assumed to be proper (also called circularly symmetric). Rather, we stress the fact that the analytic signal constructed from a nonstationary real signal is in general improper, which means that its complementary correlation function is nonzero. We explore the consequences of this finding in...

In this paper, we characterize all analytic signals with band-limited amplitudes and polynomial phases. We show that a signal with band-limited amplitude and polynomial phase is analytic if and only if it has nonneg-ative constant instantaneous frequency, i.e., the derivative of the phase is a nonnegative constant, and the constant is greater than or equal to the minimum bandwidth of the amplit...

in this paper some new applications of empirical mode decomposition (emd) and hilbert spectrum in seismic ground-roll attenuation, random noise attenuation and spectral decomposition are introduced. hilbert spectrum is a time-frequency representation for hilbert-huang transform which is obtained by combination of instantaneous frequency (if) concept and intrinsic mode function of empirical mode...

Hilbert Huang Transform is a new developed method for signal processing especially suitable for non-stationary signal processing. In this paper, we propose a two dimensional Hilbert-Huang Transform based on Bidimensional Empirical Mode Decomposition (BEMD) and quaternionic analytic signal. Bidimensional Empirical Mode Decomposition is adaptive signal decomposition method and its decomposition r...