Related papers: Information Transmission using the Nonlinear Fouri…
To comprehensively assess optical fiber communication system conditions, it is essential to implement joint estimation of the following four critical impairments: nonlinear signal-to-noise ratio (SNRNL), optical signal-to-noise ratio…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
Optimizing modulation and detection strategies for a given channel is critical to maximize the throughput of a communication system. Such an optimization can be easily carried out analytically for channels that admit closed-form analytical…
In this paper, numerical methods are suggested to compute the discrete and the continuous spectrum of a signal with respect to the Zakharov-Shabat system, a Lax operator underlying numerous integrable communication channels including the…
This paper is devoted to a discussion of the Discrete Fourier Transform (DFT) representation of a chaotic finite-duration sequence. This representation has the advantage that is itself a finite-duration sequence corresponding to samples…
The concept of Nonlinear dispersion relation (NDR) is used in various fields of Physics (nonlinear optics, hydrodynamics, hydroelasticity, mechanics, quantum optics, plasma physics,...) to characterize fundamental phenomena induced by…
The increasing complexity of neural networks and the energy consumption associated with training and inference create a need for alternative neuromorphic approaches, e.g. using optics. Current proposals and implementations rely on physical…
In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear…
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
The numerical simulation of wave propagation in semiclassical (high-frequency) problems is well known to pose a formidable challenge. In this work, a new phase-space approach for the numerical simulation of semiclassical wave propagation,…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
A simple least-squares optimisation enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an…
A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, non mirror-symmetric model described by the one-dimensional Discrete Nonlinear Schreodinger equation with…
Transfer learning (TL) is a powerful tool for enhancing the performance of neural networks (NNs) in applications such as weather and climate prediction and turbulence modeling. TL enables models to generalize to out-of-distribution data…
Optical turbulence modelling and simulation are crucial for developing astronomical ground-based instruments, laser communication, laser metrology, or any application where light propagates through a turbulent medium. In the context of…
The plane wave method is most widely used for solving the Kohn-Sham equations in first-principles materials science computations. In this procedure, the three-dimensional (3-dim) trial wave functions' fast Fourier transform (FFT) is a…
Plasmon-induced transparency (PIT) displays complex nonlinear dynamics that find critical phenomena in areas such as nonlinear waves. However, such a nonlinear solution depends sensitively on the selection of parameters and different…
We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…