Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies have considered dynamical processes that explicitly account for such higher-order dependencies, e.g., in the context of epidemic spreading processes or opinion formation. In this chapter, we focus on a closely related, but distinct third perspective: how can we use higher-order relationships to process signals and data supported on higher-order network structures. In particular, we survey how ideas from signal processing of data supported on regular domains, such as time series or images, can be extended to graphs and simplicial complexes. We discuss Fourier analysis, signal denoising, signal interpolation, and nonlinear processing through neural networks based on simplicial complexes. Key to our developments is the Hodge Laplacian matrix, a multi-relational operator that leverages the special structure of simplicial complexes and generalizes desirable properties of the Laplacian matrix in graph signal processing.

xvi, 751 hlm, ilust : 25 c

Olfaction, the sense of smell, has received scant attention from a signal processing perspective in comparison to audition and vision. In this paper, we develop a signal processing paradigm for olfactory signals based on new scientific discoveries including the psychophysics concept of olfactory white. We describe a framework for predicting the perception of odorant compounds from their physicochemical features and use the prediction as a foundation for several downstream processing tasks. We detail formulations for odor cancellation and food steganography, and provide real-world empirical examples for the two tasks. We also discuss adaptive filtering and other olfactory signal processing tasks at a high level.

Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing framework that relates a graph shift operator or filter on a subgraph with a filter on the ambient graph through an operator loss. It allows us to define shift operators for the subgraph signal, which has a meaningful interpretation and relation to mixtures of shift invariant filters restricted to different subgraphs of the ambient graph (which we call semi shift invariant). This leads to a notion of frequency domain for the subgraph signal consistent in some sense with that of the full graph signal. We apply the subgraph signal processing machinery to several applications and demonstrate the utility of this framework in cases where only partial graph signals are observed.

xiv,564 hlm , ilust : 224 c

Electroencephalography (EEG) is an non-invasive method to record the electrical activity of the brain. The EEG signals are low bandwidth and recorded from multiple electrodes simultaneously in a time synchronized manner. Typical EEG signal processing involves extracting features from all the individual channels separately and then fusing these features for downstream applications. In this paper, we propose a signal transformation, using basic signal processing, to combine the individual channels of a low-bandwidth signal, like the EEG into a single-channel high-bandwidth signal, like audio. Further this signal transformation is bi-directional, namely the high-bandwidth single-channel can be transformed to generate the individual low-bandwidth signals without any loss of information. Such a transformation when applied to EEG signals overcomes the need to process multiple signals and allows for a single-channel processing. The advantage of this signal transformation is that it allows the use of pre-trained single-channel pre-trained models, for multi-channel signal processing and analysis. We further show the utility of the signal transformation on publicly available EEG dataset.

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogs to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.

xix, 796, Ilust : 24 c

Higher-order networks can sustain topological signals which are variables associated not only to the nodes, but also to the links, to the triangles and in general to the higher dimensional simplices of simplicial complexes. These topological signals can describe a large variety of real systems including currents in the ocean, synaptic currents between neurons and biological transportation networks. In real scenarios topological signal data might be noisy and an important task is to process these signals by improving their signal to noise ratio. So far topological signals are typically processed independently of each other. For instance, node signals are processed independently of link signals, and algorithms that can enforce a consistent processing of topological signals across different dimensions are largely lacking. Here we propose Dirac signal processing, an adaptive, unsupervised signal processing algorithm that learns to jointly filter topological signals supported on nodes, links and triangles of simplicial complexes in a consistent way. The proposed Dirac signal processing algorithm is formulated in terms of the discrete Dirac operator which can be interpreted as "square root" of a higher-order Hodge Laplacian. We discuss in detail the properties of the Dirac operator including its spectrum and the chirality of its eigenvectors and we adopt this operator to formulate Dirac signal processing that can filter noisy signals defined on nodes, links and triangles of simplicial complexes. We test our algorithms on noisy synthetic data and noisy data of drifters in the ocean and find that the algorithm can learn to efficiently reconstruct the true signals outperforming algorithms based exclusively on the Hodge Laplacian.

Over the past decade, storage channels have undergone a steady increase in capacity. With the prediction of achieving 10 Tb/in2 areal density for magnetic recording channels in sight, the industry is pushing towards di erent technologies for storage channels. Heat-assisted magnetic recording, bit-patterned media, and twodimensional magnetic recording (TDMR) are cited as viable alternative technologies to meet the increasing market demand. Among these technologies, the twodimensional magnetic recording channel has the advantage of using conventional medium while relying on improvement from signal processing. Capacity approaching codes and detection methods tailored to the magnetic recording channels are the main signal processing tools used in magnetic recording. The promise is that two-dimensional signal processing will play a role in bringing about the theoretical predictions. The main challenges in TDMR media are as follows: i) the small area allocated to each bit on the media, and the sophisticated read and write processes in shingled magnetic recording devices result in signi cant amount of noise, ii) the twodimensional inter-symbol interference is intrinsic to the nature of shingled magnetic recording. Thus, a feasible two-dimensional communication system is needed to combat the errors that arise from aggressive read and write processes. In this dissertation, we present some of the work done on signal processing aspect for storage channels. We discuss i) the nano-scale model of the storage channel, ii) noise characteristics and corresponding detection strategies, iii) two-dimensional signal processing targeted at shingled magnetic recording

Our paper presents an attempt to axiomatise signal processing. Our long-term goal is to formulate signal processing algorithms for an ideal world of exact computation and prove properties about them, then interpret these ideal formulations and apply them without change to real world discrete data. We give models of the axioms that are based on Gaussian functions, that allow for exact computations and automated tests of signal algorithm properties.

Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon Fourier transform and linear shift invariant graphon filters, the graphon counterparts of the graph Fourier transform and graph filters. It is shown that for convergent sequences of graphs and associated graph signals: (i) the graph Fourier transform converges to the graphon Fourier transform when the graphon signal is bandlimited; (ii) the spectral and vertex responses of graph filters converge to the spectral and vertex responses of graphon filters with the same coefficients. These theorems imply that for graphs that belong to certain families, i.e., that are part of sequences that converge to a certain graphon, graph Fourier analysis and graph filter design have well defined limits. In turn, these facts extend applicability of graph signal processing to graphs with large number of nodes -- since signal processing pipelines designed for limit graphons can be applied to finite graphs -- and to dynamic graphs -- since we can relate the result of SP pipelines designed for different graphs from the same convergent graph sequence.

Joint communication and radar sensing (JCR) represents an emerging research field aiming to integrate the above two functionalities into a single system, by sharing the majority of hardware, signal processing modules and, in a typical case, the transmitted signal. The close cooperation of the communication and sensing functions can enable significant improvement of spectrum efficiency, reduction of device size, cost and power consumption, and improvement of performance of both functions. Advanced signal processing techniques are critical for making the integration efficient, from transmission signal design to receiver processing. This paper provides a comprehensive overview of the state-of-the-art on JCR systems from the signal processing perspective. A balanced coverage on both transmitter and receiver is provided for three types of JCR systems, namely, communication-centric, radar-centric, and joint design and optimization.

Sequences upstream of the coding region in prokaryotes show a consensus sequence called the Shine Dalgarno sequence. This sequence is the Watson-Crick complement to the 3' tail of 16S ribosomal RNA. Rosnick analyzed the ensemble free energy scores between the 3' tail-end of the RNA and the underlying mRNA. He found that the affinity between the tail-end and the mRNA is not just restricted to the upstream Shine Dalgarno region (SD region), but also extends downstream throughout the length of the gene. He confirmed the SD region as the lock signal and found an ensemble periodic free energy signal called the synchronization signal in the downstream region with a harmonic that peaks every third nucleotide with respect to the start codon. The periodic signal is hypothesized to either have a role in keeping the ribosome in frame with the mRNA being translated, or being a good predictive indicator of that state. The current work: •Studies the hypothesis that the lock and the periodic signal seen in the ensemble of the species coding regions extends beyond just E.coli. Specifically the work is concerned with analysis of sample of species across bacteria and archae kingdoms of the prokaryotes. The analysis shows that the periodic signal is present in the coding regions but not in the non-coding regions and that in some cases a lock signal is not present. This work proposes an Exponential Binding Index Locking Model to account for the genes with no upstream lock signal. •Proposes a novel methodology for analysis of the synchronization signal over individual genes. The approach leverages the ensemble periodicity information through sinusoidal wave interpolation with frequency of 1/3rd to approximate the synchronization signal and study its magnitude and phase characteristics. The synchronization signal is seen as a good indicator of the process of translation as suggested by our investigations. The starting phase of the signal is dependent on the frame in which the Shine Dalgarno lock, where present happens upstream of start. An application of individual synchronization signal is identification of frameshifts in general in genes.The +1 programmed frameshifting gene prfB of E.Coli K12 was used as a case study to demonstrate this application

Frequency is a central concept in Mathematics, Physics, and Signal Processing. It is the main tool for describing the oscillatory behavior of signals, which is usually argued to be the manifestation of some of their key features, depending on their nature. For instance, this is the case of Electroencephalographic signals. Hence, frequency is substantially present in the most common methodologies for analyzing signals, as the Fourier Analysis or the Time-Frequency Analysis. However, in spite of its importance as a keystone in Signal Processing, and its seemingly simple meaning, its mathematical foundation is not as straightforward as it may seem at first glance. A naive interpretation of the different mathematical concepts modelling frequency can be misleading, as their actual meanings essentially differ from the intuitive notion which are supposed to represent. In our opinion, this circumstance should be taken into account in order to develop appropriate signal analyzing and processing tools in some applications. In the current text we discuss this topic, with the main goal to draw the attention of the mathematical and engineering community to this point,often overlooked.

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that |P|≤1, a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 107. We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ-approximate fractional query problem that requires O((1/δ)+log(1/ϵ)) queries to perform where O(1/δ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O(dlogN+log2N) 1 and 2-qubit gates for a filter of lengths d. Published by the American Physical Society 2024

openThe thesis suggests a solution for a coding system that, like QR codes, conveys messages through audio signals. This project, done in partnership with a startup that developed the application called TISCODE, aimed to establish a reliable data transmission method using various techniques, including the spectrogram and Solomon codes for error correction. The system underwent testing in multiple noisy environments to assess its effectiveness. The study concludes with an analysis of the current application status and a discussion on potential future enhancements

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and phi generalizes the concept of the z-transform to bijective linear mappings from a vector space of, e.g., signal samples, into the module M. A signal model provides the structure for a particular linear signal processing application, such as infinite and finite discrete time, or infinite or finite discrete space, or the various forms of multidimensional linear signal processing. As soon as a signal model is chosen, basic ingredients follow, including the associated notions of filtering, spectrum, and Fourier transform. The shift operator is a key concept in the algebraic theory: it is the generator of the algebra of filters A. Once the shift is chosen, a well-defined methodology leads to the associated signal model. Different shifts correspond to infinite and finite time models with associated infinite and finite z-transforms, and to infinite and finite space models with associated infinite and finite C-transforms (that we introduce). In particular, we show that the 16 discrete cosine and sine transforms are Fourier transforms for the finite space models. Other definitions of the shift naturally lead to new signal models and to new transforms as associated Fourier transforms in one and higher dimensions, separable and non-separable. We explain in algebraic terms shift-invariance (the algebra of filters A is commutative), the role of boundary conditions and signal extensions, the connections between linear transforms and linear finite Gauss-Markov fields, and several other concepts and connections.

A robust digital image watermarking scheme based on singular value decomposition (SVD) and a tiny genetic algorithm (Tiny-GA) is proposed in this paper. Previous works have shown that both one-way and non-symmetric properties of SVD make it desirable for watermarking techniques. The produced singular values are very stable and vary very little under various image processing operations or attacks. In the proposed scheme, the singular values of a cover image are modified by multiple scale factors to embed the watermark image. Since the values of scale factors determine the watermark strength; therefore, we use the Tiny-GA to search the proper values in order to improve the visual quality of the watermarked image and the robustness of the watermark. Experimental results demonstrate that our scheme is able to withstand a variety of image processing attacks.

Extremely large-scale multiple-input-multiple-output (XL-MIMO), which offers vast spatial degrees of freedom, has emerged as a potentially pivotal enabling technology for the sixth generation (6G) of wireless mobile networks. With its growing significance, both opportunities and challenges are concurrently manifesting. This paper presents a comprehensive survey of research on XL-MIMO wireless systems. In particular, we introduce four XL-MIMO hardware architectures: uniform linear array (ULA)-based XL-MIMO, uniform planar array (UPA)-based XL-MIMO utilizing either patch antennas or point antennas, and continuous aperture (CAP)-based XL-MIMO. We comprehensively analyze and discuss their characteristics and interrelationships. Following this, we introduce several electromagnetic characteristics and general distance boundaries in XL-MIMO. Given the distinct electromagnetic properties of near-field communications, we present a range of channel models to demonstrate the benefits of XL-MIMO. We further discuss and summarize signal processing schemes for XL-MIMO. It is worth noting that the low-complexity signal processing schemes and deep learning empowered signal processing schemes are reviewed and highlighted to promote the practical implementation of XL-MIMO. Furthermore, we explore the interplay between XL-MIMO and other emergent 6G technologies. Finally, we outline several compelling research directions for future XL-MIMO wireless communication systems.