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Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…
Time-frequency images (TFIs) provide a joint time-frequency representation of a signal and have become an effective tool for analyzing, characterizing, and processing non-stationary signals. Deep learning (DL) techniques have become…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
A time-frequency diagram is a commonly used visualization for observing the time-frequency distribution of radio signals and analyzing their time-varying patterns of communication states in radio monitoring and management. While it excels…
Frequency-domain performance analysis of intersample behavior in sampled-data and multirate systems is challenging due to the lack of a frequency-separation principle, and systematic identification techniques are lacking. The aim of this…
Nonlinear metasurfaces that dynamically manipulate the phase of a passing light beam are of interest for a wide range of applications. The controlled operation of such devices requires accurate measurements of the optical transmission phase…
We prove Hilbert transform identities involving conformal maps via the use of Rellich identity and the solution of the Neumann problem in a graph Lipschitz domain in the plane. We obtain as consequences new $L^2$-weighted estimates for the…
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially…
Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific…
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embedding. Such hierarchical structure can be global in the data…
This work proposes and study the concept of Functional Data Analysis transform, applying it to the performance improving of volumetric Bouligand-Minkowski fractal descriptors. The proposed transform consists essentially in changing the…
Fourier transformations of several functions of one and two variables are evaluated and then used to derive some integral and series identities. It is shown that certain double Mordell integrals can be reduced to a sum of products of…
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…
From a time series whose data are embedded in heavy noise, we construct an Hilbert space operator (J-operator) whose discrete spectrum represents the signal while the essential spectrum located on the unit circle, is associated with the…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines. Here we present a novel approach, based on the Hilbert transform (HT). We show that temporal…
We propose two experiments suited for high school and/or undergraduate physics laboratory which are aimed to the discovery of the practical meaning and usefulness of the FFT analysis as a mathematical and graphical instrument, intended to…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
Usually, the dynamics of linear time-invariant systems described by an integral operator of convolution type, which is defined in the Hilbert space of Lebesgue square integrable functions on the whole line. Such a description leads to…
Transient signals are often composed of a series of modes that have multivalued time-dependent instantaneous frequency (IF), which brings challenges to the development of signal processing technology. Fortunately, the group delay (GD) of…