Related papers: The hyperanalytic signal
A common signal is defined for any two signals which have non-zero correlation. A mathematical method is provided to extract the best obtainable common signal between the two signals. This analysis is extended to extracting common signal…
The classical Hamilton equations are reinterpreted by means of complex analysis, in a non standard way. This suggests a natural extension of the Hamilton equations to the quaternionic case, extension which coincides with the one introduced…
We demonstrate superadditivity in the communication capacity of a binary alphabet consisting of two nonorthogonal quantum states. For this scheme, collective decoding is performed two transmissions at a time. This improves upon the previous…
The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…
The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the…
Quantum Monte Carlo method is used to re-examine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a `correlated pairing', $\langle \tilde{c}_{i\uparrow}…
It is shown that the copropagating three-wave-mixing parametric process, with appropriate type-II extended phase matching and pumped with a short second-harmonic pulse, can perform spectral phase conjugation and parametric amplification,…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
Many physical systems can be adequately modelled using a second order approximation. The problem of plant identification reduces to the problem of estimating the position of a single pair of complex conjugate poles. One approach to the…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on a tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their…
A scheme to a complex-valued acquisition of the Fourier transform imaging was proposed. The main idea is to project the real and the imaginary parts of a diffraction field to intensity distributions respectively. The whole procedure was…
One of the fundamental problems in communications is finding the energy distribution of signals in time and frequency domains. It should, therefore, be of great interest to find the most energy concentration hypercomplex signal. The present…
The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two…
We introduce an extension of hamiltonian dynamics, defined on hyperkahler manifolds, which we call ``hyperhamiltonian dynamics''. We show that this has many of the attractive features of standard hamiltonian dynamics. We also discuss the…
Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric…
Fast algorithms for arithmetic on real or complex polynomials are well-known and have proven to be not only asymptotically efficient but also very practical. Based on Fast Fourier Transform (FFT), they for instance multiply two polynomials…
The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms -- the…
Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a…