Signal Processing Problems Research Articles

A Time-Frequency Domain Analysis Method for Variable Frequency Hopping Signal.

A variable frequency hopping (VFH) signal is a kind of frequency hopping (FH) signal that varies both in frequency and dwell time. However, in radio surveillance, the existing methods for unidentified signals using VFH cannot be effectively handled. In this paper, we proposed an improved joint analysis method based on time-frequency domain features, which adopts multi-level processing to solve the time-frequency domain feature analysis problem of the VFH signal. First, the received signal is pre-processed by Short-Time Fourier Transform (STFT) and binarization, and a highly discriminative time-frequency image is obtained; then, the fixed frequency signal is removed based on the feature of connected domains, and the conventional frequency hopping (CFH) signal is removed by density-based spatial clustering of applications with noise (DBSCAN); finally, the overlapping region is cropped by the joint energy peak time-domain continuity properties. After the above multi-level joint processing method, the problem of VFH signal processing is effectively solved. The simulation result shows that the Mean Square Error (MSE) between the output results and the time-frequency image of the original VFH signal tends to be close to 0 when the Signal-to-Noise ratio (SNR) is 5 dB.

Analysis and comparison of high-performance computing solvers for minimisation problems in signal processing

Several physics and engineering applications involve the solution of a minimisation problem to compute an approximation of the input signal. Modern hardware and software use high-performance computing to solve problems and considerably reduce execution time. In this paper, different optimisation methods are compared and analysed for the solution of two classes of non-linear minimisation problems for signal approximation and denoising with different constraints and involving computationally expensive operations, i.e., (i) the global optimisers divide rectangle-local and the improved stochastic ranking evolution strategy, and (ii) the local optimisers principal axis, the Limited-memory Broyden, Fletcher, Goldfarb, Shanno, and the constrained optimisation by linear approximations. The proposed approximation and denoising minimisation problems are attractive due to their numerical and analytical properties, and their analysis is general enough to be extended to most signal-processing problems. As the main contribution and novelty, our analysis combines an efficient implementation of signal approximation and denoising on arbitrary domains, a comparison of the main optimisation methods and their high-performance computing implementations, and a scalability analysis of the main algebraic operations involved in the solution of the problem, such as the solution of linear systems and singular value decomposition. Our analysis is also general regarding the signal processing problem, variables, constraints (e.g., bounded, non-linear), domains (e.g., structured and unstructured grids, dimensionality), high-performance computing hardware (e.g., cloud computing, homogeneous vs. heterogeneous). Experimental tests are performed on the CINECA Marconi100 cluster at the 26th position in the “top500” list and consider several parameters, such as functional computation, convergence, execution time, and scalability. Our experimental tests are discussed on real-case applications, such as the reconstruction of the solution of the fluid flow field equation on an unstructured grid and the denoising of a satellite image affected by speckle noise. The experimental results show that principal axis is the best optimiser in terms of minima computation: the efficiency of the approximation is 38% with 256 processes, while the denoising has 46% with 32 processes.

An Efficient Numerical Algorithm for Abnormal Integrals with Arbitrary Order Double Bessel Functions of the First Type

Abstract The integrals of the first type of double Bessel functions have a wide range of applications in geological exploration, mechanical and electromagnetic responses, signal processing, scattering, and wetting. In this paper, we develop a linear transformation accelerated convergence algorithm (LTACA) that combines the large argument approximate expression of the Bessel function (LAAEBF) and the integral accumulation to provide an efficient numerical algorithm for abnormal integrals with arbitrary order double Bessel functions of the first type. The effectiveness and high efficiency of the algorithm are verified by numerical examples, and its high accuracy is demonstrated by comparison with the Gaver-Stehfest inverse Laplace transform method (GSILTM). This offers a reliable and efficient computational method for the study of signal processing and mechanical problems.

Convergence of Peaceman-Rachford splitting method with Bregman distance for three-block nonconvex nonseparable optimization

Abstract It is of strong theoretical significance and application prospects to explore three-block nonconvex optimization with nonseparable structure, which are often modeled for many problems in machine learning, statistics, and image and signal processing. In this article, by combining the Bregman distance and Peaceman-Rachford splitting method, we propose a novel three-block Bregman Peaceman-Rachford splitting method (3-BPRSM). Under a general assumption, global convergence is presented via optimality conditions. Furthermore, we prove strong convergence when the augmented Lagrange function satisfies Kurdyka-Łojasiewicz property. In addition, if the association function possessing the Kurdyka-Łojasiewicz property exhibits a distinctive structure, then linear and sublinear convergence rate of 3-BPRSM can be guaranteed. Finally, a preliminary numerical experiment demonstrates the effectiveness.

Vocal Call Locator Benchmark (VCL) for localizing rodent vocalizations from multi-channel audio.

Understanding the behavioral and neural dynamics of social interactions is a goal of contemporary neuroscience. Many machine learning methods have emerged in recent years to make sense of complex video and neurophysiological data that result from these experiments. Less focus has been placed on understanding how animals process acoustic information, including social vocalizations. A critical step to bridge this gap is determining the senders and receivers of acoustic information in social interactions. While sound source localization (SSL) is a classic problem in signal processing, existing approaches are limited in their ability to localize animal-generated sounds in standard laboratory environments. Advances in deep learning methods for SSL are likely to help address these limitations, however there are currently no publicly available models, datasets, or benchmarks to systematically evaluate SSL algorithms in the domain of bioacoustics. Here, we present the VCL Benchmark: the first large-scale dataset for benchmarking SSL algorithms in rodents. We acquired synchronized video and multi-channel audio recordings of 767,295 sounds with annotated ground truth sources across 9 conditions. The dataset provides benchmarks which evaluate SSL performance on real data, simulated acoustic data, and a mixture of real and simulated data. We intend for this benchmark to facilitate knowledge transfer between the neuroscience and acoustic machine learning communities, which have had limited overlap.

Terminological features of the concept of signal-to-noise ratio when processing ultra-wideband signals

Currently, when processing various signals and studying various types of receivers, there are many definitions for one of the basic characteristics of radio systems – signal-to-noise ratio (SNR). At the same time, the terminological feature of the SNR concept is that any definition within the framework of a locally solvable signal processing problem is correct. However, difficulties arise when comparing the effectiveness of one algorithm with another, when studying different signal models, or when measuring the SNR in different parts of the receiving system. Some researchers ignore this fact due to the apparent absolute clarity of this issue, which leads to incorrect comparison of various processing algorithms or the formation of obviously unrealizable requirements for the designed equipment. In each locally solved problem, the determination of SNR will be individual, and comparison of efficiency at a fixed SNR must be carried out with mandatory scaling of signal energies depending on the formulation of the problem. This paper systematizes the terminological features of the SNR concept in order to ensure uniformity of its application by researchers and engineers. The purpose of the work is to systematize the definition of SNR for various signal models and conditions for measuring this characteristic, to specify the results in terms of terminological features of UWB signal processing and to propose a model for recalculating the SNR depending on the stage of the signal transmission and reception process. The paper examines the determination of SNR at the input and output of optimal and matched filters, at the output of optimal receivers operating under conditions of various a priori uncertainties, as well as when processing various classes of signals. By determining the SNR at the output of the matched filter and the SNR at the output of the maximum likelihood receiver for a rectangular video pulse, the discrepancy between the signal energies, all other things being equal, is clearly demonstrated. A connection has been established between the SNR when processing ultra-wideband signals at the output of the optimal receiver with similar devices for processing other types of signals, as well as with the SNR at the input of the receiving system. Systematization of the terminological features of the SNR concept will allow theoretical researchers to choose SNR definitions that are as close as possible to practical applications when analyzing the effectiveness of synthesized algorithms, and will allow practicing engineers to correctly interpret the results of theoretical calculations when developing or testing radio engineering systems.

Computer vision quickly identifies radio signals with unlimited accuracy

A seminal component of systems thinking is the application of an advanced technology in one domain to solve a challenging problem in a different domain. This article introduces a method of using advanced computer vision to solve the challenging signal processing problem of specific emitter identification. A one-dimensional signal is sampled; those samples are transformed into to two-dimensional images by computing a bispectrum; those images are evaluated using advanced computer vision; and the results are statistically combined until any user-selected level of classification accuracy is obtained. In testing on a published DARPA challenge dataset, for every eight additional signal samples taken from a candidate signal (out of many thousands), classification error decreases by an entire order of magnitude.

Gegenbauer Graph Neural Networks for Time-Varying Signal Reconstruction.

Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series forecasting. Accurately capturing the spatio-temporal information inherent in these signals is crucial for effectively addressing these tasks. However, existing approaches relying on smoothness assumptions of temporal differences and simple convex optimization techniques that have inherent limitations. To address these challenges, we propose a novel approach that incorporates a learning module to enhance the accuracy of the downstream task. To this end, we introduce the Gegenbauer-based graph convolutional (GegenConv) operator, which is a generalization of the conventional Chebyshev graph convolution by leveraging the theory of Gegenbauer polynomials. By deviating from traditional convex problems, we expand the complexity of the model and offer a more accurate solution for recovering time-varying graph signals. Building upon GegenConv, we design the Gegenbauer-based time graph neural network (GegenGNN) architecture, which adopts an encoder-decoder structure. Likewise, our approach also uses a dedicated loss function that incorporates a mean squared error (MSE) component alongside Sobolev smoothness regularization. This combination enables GegenGNN to capture both the fidelity to ground truth and the underlying smoothness properties of the signals, enhancing the reconstruction performance. We conduct extensive experiments on real datasets to evaluate the effectiveness of our proposed approach. The experimental results demonstrate that GegenGNN outperforms state-of-the-art methods, showcasing its superior capability in recovering time-varying graph signals.

Avoiding Post-Processing With Event-Based Detection in Biomedical Signals.

Finding events of interest is a common task in biomedical signal processing. The detection of epileptic seizures and signal artefacts are two key examples. Epoch-based classification is the typical machine learning framework to detect such signal events because of the straightforward application of classical machine learning techniques. Usually, post-processing is required to achieve good performance and enforce temporal dependencies. Designing the right post-processing scheme to convert these classification outputs into events is a tedious, and labor-intensive element of this framework. We propose an event-based modeling framework that directly works with events as learning targets, stepping away from ad-hoc post-processing schemes to turn model outputs into events. We illustrate the practical power of this framework on simulated data and real-world data, comparing it to epoch-based modeling approaches. We show that event-based modeling (without tailored post-processing) performs on par with or better than epoch-based modeling with extensive post-processing. These results show the power of treating events as direct learning targets, instead of using ad-hoc post-processing to obtain them, severely reducing design effort. Significance The event-based modeling framework can easily be applied to other event detection problems in signal processing, removing the need for intensive task-specific post-processing.

Ionograms Trace Extraction Method Based on Multiscale Transformer Network

The echo traces in the ionograms contain key information about the ionosphere. Therefore, the accurate extraction of these traces is crucial for the subsequent work. This paper transforms the original signal processing problem into a semantic segmentation task, combines it with the currently popular deep learning techniques, and proposes a multiscale Transformer network to achieve pixel-level trace extraction. To train the proposed model, we built a dataset by discretizing the original echo data, labeling, and other preprocessing work. A series of advanced semantic segmentation networks are utilized for comparative experiments. The analysis of the results indicates that the proposed network excels in performance, achieving the highest scores on key semantic segmentation evaluation metrics, including mIoU, Kappa, Dice, and AUC-ROC. In addition, this paper also designs a series of ablation experiments to observe the changes in network performance and to evaluate the rationality of the network design. The experimental results demonstrate the effectiveness of the network in the trace extraction task, which plays a positive role in the subsequent electron density reversal work.

Sequential inertial linear ADMM algorithm for nonconvex and nonsmooth multiblock problems with nonseparable structure

The alternating direction method of multipliers (ADMM) has been widely used to solve linear constrained problems in signal processing, matrix decomposition, machine learning, and many other fields. This paper introduces two linearized ADMM algorithms, namely sequential partial linear inertial ADMM (SPLI-ADMM) and sequential complete linear inertial ADMM (SCLI-ADMM), which integrate linearized ADMM approach with inertial technique in the full nonconvex framework with nonseparable structure. Iterative schemes are formulated using either partial or full linearization while also incorporating the sequential gradient of the composite term in each subproblem’s update. This adaptation ensures that each iteration utilizes the latest information to improve the efficiency of the algorithms. Under some mild conditions, we prove that the sequences generated by two proposed algorithms converge to the critical points of the problem with the help of KŁ property. Finally, some numerical results are reported to show the effectiveness of the proposed algorithms.

Chaff jamming recognition and suppression based on semi‐realistic dataset and Pre‐Decluttering Dual‐Stage UNet

AbstractCountermeasures for chaff jamming have drawn great attention in the field of radar target detection and tracking. Current approaches for chaff jamming recognition and suppression exhibit limitations in practical effect, generalisation ability, and hybrid jamming handling. To address the above problems, the authors first transform the traditional 1D signal processing problem into a 2D semantic segmentation task and then solve it from the perspective of the dataset construction and algorithm design. For the dataset construction, the authors use both measured and simulated data to synthesise a more realistic labelled dataset (semi‐realistic dataset), which is also with good diversity due to its adjustable chaff interference background. For the algorithm design, the authors propose a Pre‐Decluttering Dual‐Stage UNet (D2UNet) to recognise and suppress chaff jamming in two stages successively, where the former provides prior attention masks for the latter. To further improve the performance of D2UNet, the authors also design a multi‐stage loss function to achieve progressive training. Extensive experimental results demonstrate that D2UNet delivers remarkable recognition accuracy (99.305%) and suppression performance (41.326 dB peak signal‐to‐jamming ratio, 0.9952 structure similarity index measure) on the semi‐realistic dataset. Its practical effect is further verified on measured data.

Stabilized BB projection algorithm for large-scale convex constrained nonlinear monotone equations to signal and image processing problems

The Barzilai–Borwein (BB) method is a popular and efficient gradient method for solving large-scale unconstrained optimization problems. In general, it converges much faster than the steepest descent (Cauchy) method. However, it may not converge, even when the objective function is strongly convex. To overcome this, by virtue of bounding the distance between sequential iterates, [Burdakov et al. (2019)] proposed a stabilized BB method. In this paper, by combining the stabilized BB method with a projection approach, we develop a stabilized BB projection (SBBP) method to solve nonlinear monotone equations with convex constraints. SBBP does not involve computing matrices proving the usefulness for solving large-scale problems. Its global convergence and Q-linear convergence rate are also established. We report numerical experiments on recovering sparse signals and restoring blurred images arising from compressive sensing, demonstrating the usefulness of SBBP.

New graphical models for sequential data and the improved state estimations by data-conditioned driving noises

A prevalent problem in statistical signal processing, applied statistics, and time series analysis arises from the attempt to identify the hidden state of Markov process based on a set of available noisy observations. In the context of sequential data, filtering refers to the probability distribution of the underlying Markovian system given the measurements made at or before the time of the estimated state. In addition to the filtering, the smoothing distribution is obtained from incorporating measurements made after the time of the estimated state into the filtered solution. This work proposes a number of new filters and smoothers that, in contrast to the traditional schemes, systematically make use of the process noises to give rise to enhanced performances in addressing the state estimation problem. In doing so, our approaches for the resolution are characterized by the application of the graphical models; the graph-based framework not only provides a unified perspective on the existing filters and smoothers but leads us to design new algorithms in a consistent and comprehensible manner. Moreover, the graph models facilitate the implementation of the suggested algorithms through message passing on the graph.

Event detection and classification from multimodal time series with application to neural data

The detection of events in time-series data is a common signal-processing problem. When the data can be modeled as a known template signal with an unknown delay in Gaussian noise, detection of the template signal can be done with a traditional matched filter. However, in many applications, the event of interest is represented in multimodal data consisting of both Gaussian and point-process time series. Neuroscience experiments, for example, can simultaneously record multimodal neural signals such as local field potentials (LFPs), which can be modeled as Gaussian, and neuronal spikes, which can be modeled as point processes. Currently, no method exists for event detection from such multimodal data, and as such our objective in this work is to develop a method to meet this need. Here we address this challenge by developing the multimodal event detector (MED) algorithm which simultaneously estimates event times and classes. To do this, we write a multimodal likelihood function for Gaussian and point-process observations and derive the associated maximum likelihood estimator of simultaneous event times and classes. We additionally introduce a cross-modal scaling parameter to account for model mismatch in real datasets. We validate this method in extensive simulations as well as in a neural spike-LFP dataset recorded during an eye-movement task, where the events of interest are eye movements with unknown times and directions. We show that the MED can successfully detect eye movement onset and classify eye movement direction. Further, the MED successfully combines information across data modalities, with multimodal performance exceeding unimodal performance. This method can facilitate applications such as the discovery of latent events in multimodal neural population activity and the development of brain-computer interfaces for naturalistic settings without constrained tasks or prior knowledge of event times.

Efficient FPGA implementation for sound source separation using direction-informed multichannel non-negative matrix factorization

Sound source separation (SSS) is a fundamental problem in audio signal processing, aiming to recover individual audio sources from a given mixture. A promising approach is multichannel non-negative matrix factorization (MNMF), which employs a Gaussian probabilistic model encoding both magnitude correlations and phase differences between channels through spatial covariance matrices (SCM). In this work, we present a dedicated hardware architecture implemented on field programmable gate arrays (FPGAs) for efficient SSS using MNMF-based techniques. A novel decorrelation constraint is presented to facilitate the factorization of the SCM signal model, tailored to the challenges of multichannel source separation. The performance of this FPGA-based approach is comprehensively evaluated, taking advantage of the flexibility and computational capabilities of FPGAs to create an efficient real-time source separation framework. Our experimental results demonstrate consistent, high-quality results in terms of sound separation.

Generalized variational framework with minimax optimization for parametric blind deconvolution

Blind deconvolution (BD), which aims to separate unknown convolved signals, is a fundamental problem in signal processing. Due to the ill-posedness and underdetermination of the convolution system, it is a challenging nonlinear inverse problem. This paper is devoted to the algorithmic studies of parametric BD, which is typically applied to recover images from ad hoc optical modalities. We propose a generalized variational framework for parametric BD with various priors and potential functions. By using the conjugate theory in convex analysis, the framework can be cast into a nonlinear saddle point problem. We employ the recent advances in minimax optimization to solve the parametric BD by the nonlinear primal-dual hybrid gradient method, with all subproblems admitting closed-form solutions. Numerical simulations on synthetic and real datasets demonstrate the compelling performance of the minimax optimization approach for solving parametric BD.

Chebyshev filter and Butterworth filters: Comparison and applications in different cases

This study focuses on the filter selection problem in signal processing and wireless communication applications. Specifically, addressed two different filter selection problems: the Chebyshev filter and the Butterworth filter. Using MATLAB, in order to design and model these two types of filters. The performance, frequency response, transition band width, filter order, design complexity and target application of Chebyshev filter and Butterworth filter under different parameters are analyzed and compared. The selection of the two filters under different conditions and the reasons for choosing them are discussed. The Chebyshev filter is suited for applications that call for a high frequency response, and Chebyshev filters provide a steeper roll-down slope, which can suppress high-frequency noise and interference signals, according to the test results, it is widely used in communication systems. On the other hand, the Butterworth filter is more suitable for applications that require a flat passband and a wide stopband, such as audio systems.

Simulation model parameter optimization method for multidimensional signals

The paper describes an approach to minimize the number of simulation experiments of multidimensional signals by means of a regression neural network. Multivariate signal simulation systems are in demand for testing real-time computing systems, but they mostly have a wide vector of model parameters. The formation of parameter vector for the simulation model of multidimensional signals, which ensures an adequate solution to the problem of signal processing obtained as a result of the model operation, is an urgent task. The authors propose a method of heuristic optimization of input parameters, implemented by means of machine learning, which reduces the searching of values for the given optimization function. In this study the ability to perform real-time signal simulations is the optimization feature. The research outcomes are the description of the neural network, the rationale for its configuration, and the training and validation results.

New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: The IMFogram algorithm

The analysis of the time–frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative time–frequency representations of a signal each with its advantages and limitations. In this work, following the success of nonlinear methods for the decomposition of signals into intrinsic mode functions (IMFs), we first provide more theoretical insights into the so–called Iterative Filtering decomposition algorithm, proving an energy conservation result for the derived decompositions. Furthermore, we present a new time–frequency representation method based on the IMF decomposition of a signal, which is called IMFogram. We prove theoretical results regarding this method, including its convergence to the spectrogram representation for a certain class of signals, and we present a few examples of applications, comparing results with some of the most well-known approaches available in the literature.