Submit to Special Issue Submit Abstract to Special Issue Review for Mathematics Edit a Special Issue

Journal Browser

Special Issue "Novel Mathematical Methods in Signal Processing and Its Applications"

Print Special Issue Flyer
Special Issue Editors
Special Issue Information
Keywords
Published Papers

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 15 October 2023 | Viewed by 3725

Share This Special Issue

Special Issue Editors

Prof. Dr. Gordon Morison

E-Mail Website
Guest Editor

Department of Computing, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK
Interests: signal processing; data science; tensor decompositions; machine learning

Dr. Robert C. Atkinson

E-Mail Website
Guest Editor

Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XW, UK
Interests: data science; machine learning; AutoML; explainable AI
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Signal processing and machine learning are the key enablers at the heart of the technological advancements to drive developments in mobile communications, Internet of Things, FinTech, predictive maintenance, digital health and biomedical engineering. These continually evolving fields offer huge potential for the application of mathematics and statistics to develop the next generation of algorithms to ensure they are ethical, transparent, robust and explainable. It is expected that these new algorithms will expand upon and exploit mathematical methods such as tensor analysis, stochastic calculus, information theory, complex analysis, optimization, group theory and geometric methods. This Special Issue looks for novel algorithms and mathematical methods applied to signal processing applications.

Prof. Dr. Gordon Morison
Dr. Robert C. Atkinson
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2100 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

information theory
data science
tensor signal processing
graph signal processing
time-frequency decompositions
machine learning
Bayesian signal processing
image processing and computer vision
optimization methods
audio and acoustic signal processing
compressed sensing
sparse modelling
statistical signal processing
explainable AI (XAI)
causal AI

Published Papers (5 papers)

Download All Papers

Research

Jump to: Review

Open AccessArticle

Error Probability of a Coherent M-ary PSK FSO System Influenced by Phase Noise

and

Gradimir V. Milovanović

Mathematics 2023, 11(1), 121; https://doi.org/10.3390/math11010121 - 27 Dec 2022

Viewed by 571

Abstract

In this paper, we aim to develop an analytical framework for design and analysis of new generation mobile networks fronthaul/backhaul links based on the application of free-space optical (FSO) technology. Taking the receiver hardware imperfections into account, we present an efficient analytical approach in analyzing average symbol error probability (SEP) of the coherent FSO system employing M-ary phase-shift keying (PSK). Optical signal transmission is influenced by pointing errors and atmospheric turbulence. The signal intensity fluctuations caused by atmospheric turbulence are modeled by general Málaga (

M

) distribution, which takes into account the effect of multiple scattered components. We estimate the range of the signal-to-noise ratio at which the SEP floor appears, as well as the value of this non-removable error floor. The results illustrate that the effect of imperfect phase error compensation on the SEP is more critical under weaker turbulence conditions and for higher order modulation formats. Based on the analytical tools presented here, it is possible to estimate tolerable value of standard deviation of phase noise for the given value of SEP. This value of standard deviation is an important parameter in designing the phase-locked loop filter in the receiver. Full article

(This article belongs to the Special Issue Novel Mathematical Methods in Signal Processing and Its Applications)

► Show Figures

Figure 1

Open AccessArticle

A Novel Optical-Based Methodology for Improving Nonlinear Fourier Transform

and

Mathematics 2022, 10(23), 4513; https://doi.org/10.3390/math10234513 - 29 Nov 2022

Viewed by 470

Abstract

The increasing demand for bandwidth and long-haul transmission has led to new methods of signal processing and transmission in optical fiber communication systems. The nonlinear Fourier transform is one of the most recent methods proposed, and is able to represent an integrable nonlinear Schrödinger equation (NLSE) channel in terms of its continuous and discrete spectrum, to overcome the limitation of the bandwidth imposed by the Kerr effect on silica fibers. In this paper, we will propose and investigate the Boffetta-Osburne method for the direct nonlinear Fourier implementation, and the Gel’fand-Levitan-Marchenko equation for the inverse nonlinear Fourier, as only the continuous part of the nonlinear spectrum will be used to encode information. A novel methodology is proposed to improve their numerical implementation with respect to the NLSE, and we analyze in detail how the improved algorithm can be used in a real optical system, by investigating three different modulation schemes. We report increased performance transmission and consistency in the numerical results when the proposed methodology is applied. Our results show that b-modulation will increase the Q-factor by 2 dB with respect to the other two modulations. The improvement results with our proposed methodology suggest that b-modulation applied only to a continuous part of the nonlinear spectrum is a very effective method for maximizing both the transmission bandwidth and distance in optical fiber communication systems. Full article

(This article belongs to the Special Issue Novel Mathematical Methods in Signal Processing and Its Applications)

► Show Figures

Figure 1

Open AccessArticle

Nonlinear Frequency-Modulated Waveforms Modeling and Optimization for Radar Applications

Zhihuo Xu

Xiaoyue Wang

and

Yuexia Wang

Mathematics 2022, 10(21), 3939; https://doi.org/10.3390/math10213939 - 24 Oct 2022

Viewed by 542

Abstract

Conventional radars commonly use a linear frequency-modulated (LFM) waveform as the transmitted signal. The LFM radar is a simple system, but its impulse-response function produces a −13.25 dB sidelobe, which in turn can make the detection of weak targets difficult by drowning out adjacent weak target information with the sidelobe of a strong target. To overcome this challenge, this paper presents a modeling and optimization method for non-linear frequency-modulated (NLFM) waveforms. Firstly, the time-frequency relationship model of the NLFM signal was combined by using the Legendre polynomial. Next, the signal was optimized by using a bio-inspired method, known as the Firefly algorithm. Finally, the numerical results show that the advantages of the proposed NLFM waveform include high resolution and high sensitivity, as well as ultra-low sidelobes without the loss of the signal-to-noise ratio (SNR). To the authors’ knowledge, this is the first study to use NLFM signals for target-velocity improvement measurements. Importantly, the results show that mitigating the sidelobe of the radar waveform can significantly improve the accuracy of the velocity measurements. Full article

(This article belongs to the Special Issue Novel Mathematical Methods in Signal Processing and Its Applications)

► Show Figures

Figure 1

Open AccessArticle

Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain

Jesús Navarro-Moreno

Rosa M. Fernández-Alcalá

and

Juan C. Ruiz-Molina

Mathematics 2022, 10(7), 1083; https://doi.org/10.3390/math10071083 - 28 Mar 2022

Cited by 2 | Viewed by 925

Abstract

The analysis of time series in 4D commutative hypercomplex algebras is introduced. Firstly, generalized Segre’s quaternion (GSQ) random variables and signals are studied. Then, two concepts of properness are suggested and statistical tests to check if a GSQ random vector is proper or not are proposed. Further, a method to determine in which specific hypercomplex algebra is most likely to achieve, if possible, the properness properties is given. Next, both the linear estimation and prediction problems are studied in the GSQ domain. Finally, ARMA modeling and forecasting for proper GSQ time series are tackled. Experimental results show the superiority of the proposed approach over its counterpart in the Hamilton quaternion domain. Full article

(This article belongs to the Special Issue Novel Mathematical Methods in Signal Processing and Its Applications)

► Show Figures

Figure 1

Review

Jump to: Research

Open AccessFeature PaperReview

Bright Soliton Solution of the Nonlinear Schrödinger Equation: Fourier Spectrum and Fundamental Characteristics

Natanael Karjanto

Mathematics 2022, 10(23), 4559; https://doi.org/10.3390/math10234559 - 01 Dec 2022

Viewed by 491

Abstract

We derive exact analytical expressions for the spatial Fourier spectrum of the fundamental bright soliton solution for the

(1 + 1)

-dimensional nonlinear Schrödinger equation. Similar to a Gaussian profile, the Fourier transform for the hyperbolic secant shape is also shape-preserving. Interestingly, this [...] Read more.

We derive exact analytical expressions for the spatial Fourier spectrum of the fundamental bright soliton solution for the

(1 + 1)

-dimensional nonlinear Schrödinger equation. Similar to a Gaussian profile, the Fourier transform for the hyperbolic secant shape is also shape-preserving. Interestingly, this associated hyperbolic secant Fourier spectrum can be represented by a convergent infinite series, which can be achieved using Mittag–Leffler’s expansion theorem. Conversely, given the expression of the series of the spectrum, we recover its closed form by employing Cauchy’s residue theorem for summation. We further confirm that the fundamental soliton indeed satisfies essential characteristics such as Parseval’s relation and the stretch-bandwidth reciprocity relationship. The fundamental bright soliton finds rich applications in nonlinear fiber optics and optical telecommunication systems. Full article

(This article belongs to the Special Issue Novel Mathematical Methods in Signal Processing and Its Applications)

► Show Figures