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The recognition of motion patterns belongs to very important research areas related to neurology, rehabilitation, and robotics. It is based on modern sensor technologies and general mathematical methods, multidimensional signal processing, and machine learning. The present paper is devoted to the detection of features associated with accelerometric data acquired by 31 time-synchronized sensors located at different parts of the body. Experimental data sets were acquired from 25 individuals diagnosed as healthy controls and ataxic patients. The proposed method includes the application of the discrete Fourier transform for the estimation of the mean power in selected frequency bands and the use of these features for data segments classification. The study includes a comparison of results obtained from signals recorded at different positions. Evaluations are based on classification accuracy and cross-validation errors estimated by support vector machine, Bayesian, nearest neighbours (k-NN], and neural network (NN) methods. Results show that highest accuracies of 77.1%, 78.9%, 89.9%, 98.0%, and 98.5% were achieved by NN method for signals acquired from the sensors on the feet, legs, uplegs, shoulders, and head/spine, respectively, recorded in 201 signal segments. The entire study is based on observations in the clinical environment and suggests the importance of augmented reality to decisions and diagnosis in neurology.

Data Analytics on Graphs Part III: Machine Learning on Graphs, from Graph Topology to Applications

Methods of multidimensional signal processing under spatial toroidal coordinate systems configured on a set of combining sums over vector "Glory to Ukraine Star" combinatorial configurations. Base vectors are discussed, and the two theoretically grounded approaches to formation such coordinate systems in order for optimum encoding and conversion of vector signals using its unique properties, both optimum monolithic and group vector codes, and non-redundant codes are proposed. On the particular examples described the benefits of each method of coding of multidimensional signals pointing to corresponding theorems, calculations and illustrative material. Extension of the “star” combinatorial configurations opens new possibilities for the application of methods of optimized coding and processing of multidimensional signals under toroidal coordinate systems for designing modern systems of communication and development of optimized vector information technologies. The remarkable technical merits of the vector configurations, which properties hold for the same set of an optimum encoded design in varieties permutations of its terms is demonstrated, and methods for processing of two- or multidimensional vector signals based on both the optimum binary monolithic and non-redundant codes are presented. Proposed methods of multidimensional signal processing under toroidal coordinate systems provide, essentially, a new approach to generalize them to great class of optimized problems in radio-telecommunications, navigation and information technology. Moreover, the optimization embedded in the underlying combinatorial configurations. The favorable qualities of the "stars" provide breakthrough opportunities to apply them to numerous branches of science and advanced technology, with direct applications to vector data telecommunications, vector encoded design, and optimal vector information technology., Рассматриваются методы обработки многомерных сигналов в пространственном поле координатной системы тора, построенной на множестве комбинационных сумм базовых векторов комбинаторной конфигурации ``звездного'' типа, и на основе использования ее уникальных свойств предложено два теоретически обоснованных подхода к формированию тороидных систем координат для оптимального кодирования и преобразования векторных сигналов: монолитно-групповых и безизбыточных кодов. На конкретных примерах описаны преимущества каждого метода кодирования многомерных сигналов с приведением соответствующих теорем, расчетов и иллюстративного материала. Расширение класса "звездных" комбинаторных конфигураций открывает новые возможности применения методов оптимизированного кодирования и обработки многомерных сигналов в тороидных системах координат, разработки оптимизированных векторных информационных технологий, радиотехнических устройств и систем связи., Розглядаються методи опрацювання багатовимірних сигналів у просторовому полі координатної системи тора, яка побудована на множині комбінаційних сум базових векторів комбінаторної конфігурації «зіркового» типу, і на основі використання її унікальних властивостей запропоновано два теоретично обґрунтовані підходи до формування тороїдних систем координат для оптимального кодування і перетворення векторних сигналів: монолітно-групових та ненадлишкових кодів. На конкретних прикладах окреслено переваги кожного методу кодування багатовимірних сигналів з наведенням відповідних теорем, розрахунків та ілюстративного матеріалу. Розширення класу «зіркових» комбінаторних конфігурацій відкриває нові можливості застосування методів оптимізованого кодування й опрацювання багатовимірних сигналів у тороїдних системах координат, розроблення оптимізованих векторних інформаційних технологій, вдосконалення радіотехнічних пристроїв і систем зв’язку.

Dictionary learning (DL) for sparse tensor representation aims to train a set of dictionaries for each dimension using tensor samples based on the Tucker decomposition. However, their applications are limited by the fact that all the training samples must be input simultaneously, and that there is no direct way to extend the existing online DL methods for the vector-based model to the Tucker-decomposition-based model. To overcome this limitation, in this brief, we develop a Tucker-decomposition-based strategy to achieve a warm start for updating dictionaries, based on which, an online tensor DL (TDL) algorithm is proposed. The proposed algorithm processes a single new training sample at a time, such that it can be used not only for offline learning from static samples, but also for online learning from dynamic samples, under the framework of the Tucker model. When new training samples are input, only the newly added samples need to be used for retraining the dictionaries. We verify the convergence and low-complexity of the proposed algorithm via theoretical analysis as well as online learning simulations. We also perform offline learning simulations, the results of which demonstrate that our algorithm has an obvious advantage in training accuracy over existing TDL algorithms. The proposed algorithm has the potential to be used in fields such as multidimensional signal processing, compressive sensing, and machine learning.

Effective pitch estimation is very challenging task in recent research area. There are a large set of methods that have been developed in the speech processing area for the estimation of pitch. In this paper, focus on an effective pitch estimation method using Canonical Correlation Analysis (CCA). It is used for predicting IMF components from reference signals. The proposed pitch estimation algorithm dominant harmonic model enhanced the pitch peak through signal reshaping, then for on-linear and non-stationary data analysis method EMD uses to decompose the signal into a finite number of band limited signal called IMFs. Each IMF have specific frequency band. The Keele pitch reference database is considered for evaluation of the proposed method. Autocorrelation function to detect pitch period. Finally, Multivariate multidimensional statistics data analysis tools CCA is used for selecting IMF components. Then summing up IMF components for a partial reconstruction of the NACF signal except for noisy components. The reconstructed signal contains less noise. We estimated pitch from the reconstructed signal. The performance of the proposed pitch estimation is compared in terms of Gross Pitch Error (% GPE) with existing algorithms. Pitch is an important speech parameter for a wide range of applications such as speech coding, text to speech synthesis, speech recognition, gender identification, accent identification, accent synthesis, speaker identification, speaker verification, and so on.

Mining algorithms for Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCEMRI) of breast tissue are discussed. The algorithms are based on recent advances in multidimensional signal processing and aim to advance current state‐of‐the‐art computer‐aided detection and analysis of breast tumours when these are observed at various states of development. The topics discussed include image feature extraction, information fusion using radiomics, multi‐parametric computer‐aided classification and diagnosis using information fusion of tensorial datasets as well as Clifford algebra based classification approaches and convolutional neural network deep learning methodologies. The discussion also extends to semi‐supervised deep learning and self‐supervised strategies as well as generative adversarial networks and algorithms using generated confrontational learning approaches. In order to address the problem of weakly labelled tumour images, generative adversarial deep learning strategies are considered for the classification of different tumour types. The proposed data fusion approaches provide a novel Artificial Intelligence (AI) based framework for more robust image registration that can potentially advance the early identification of heterogeneous tumour types, even when the associated imaged organs are registered as separate entities embedded in more complex geometric spaces. Finally, the general structure of a high‐dimensional medical imaging analysis platform that is based on multi‐task detection and learning is proposed as a way forward. The proposed algorithm makes use of novel loss functions that form the building blocks for a generated confrontation learning methodology that can be used for tensorial DCE‐MRI. Since some of the approaches discussed are also based on time‐lapse imaging, conclusions on the rate of proliferation of the disease can be made possible. The proposed framework can potentially reduce the costs associated with the interpretation of medical images by providing automated, faster and more consistent diagnosis.

A new method for multidimensional digital signal processing for Printed Circuit Boards (PCB) testing is described. The considered method comes to solve such problems as competition and synchronization, which are present in the multidimensional signals processing. The solution is achieved by performing in parallel all operations, replacing the analog-to-digital conversion (ADC) with differentiation operations and analyzing the signal variation rate based on the Fuzzy logic elements. As a result of these operations, using digital integration models, binary code streams are obtained that allow the reconstruction of the signal shape. Mathematical models applied for the transformation and processing of multidimensional signals are presented. The designed system for the multidimensional signal processing consists of a computing unit, the test signals generator, the data storage unit, the Printed Circuit Board with nodes for test signals application and retrieval, and finally the processing elements for differentiation and analysis based on Fuzzy logic.

Time-resolved multispectral imaging has recently found many applications ranging from biomedical to environmental field. Multidimensional approach measuring spectral and ultrafast temporal dynamics of fluorescence signal combined with spatial information (imaging) allows one to characterize biological processes at both microscopic and macroscopic level, representing a fundamental step towards development of diagnostic strategies. Long acquisition time is the main drawback of multidimensional approach because it is not compatible with biological system dynamics. In order to reduce the measurement times, it is necessary to parallelize the acquisition (hardware level) and to optimize the acquisition strategy to reduce the measurements number while preserving the information content. In this work we have developed a time-resolved multispectral fluorescence imaging system based on a spad array combined with compression techniques which allows to reduce the number of time-resolved acquisitions by a factor < 70%. The system is based on a double DMD configuration (excitation and detection) coupled to a 32x1 SPAD array, each one with its own TCSPC circuit, placed after an imaging spectrometer. This allows one to use the spatial modulation of the excitation/detection light to acquire images at different wavelengths following the single pixel camera (SPC) scheme. In order to compress the number of acquisitions, a CW fluorescence image is acquired through a CCD and Hadamard transform is applied to select most significative coefficients. The patterns related to these coefficients are subsequently used for SPC acquisition for time and spectral resolution. A Total-Variation based algorithm is used for the reconstruction of the 4D images.

Neural networks are a subset of the field of artificial intelligence (AI). The predominant types of neural networks used for multidimensional signal processing are deep convolutional neural networks (CNNs). The term deep refers generically to networks having from a "few" to several dozen or more convolution layers, and deep learning refers to methodologies for training these systems to automatically learn their functional parameters using data representative of a specific problem domain of interest. CNNs are currently being used in a broad spectrum of application areas, all of which share the common objective of being able to automatically learn features from (typically massive) data bases and to generalize their responses to circumstances not encountered during the learning phase. Ultimately, the learned features can be used for tasks such as classifying the types of signals the CNN is expected to process. The purpose of this "Lecture Notes" article is twofold: 1) to introduce the fundamental architecture of CNNs and 2) to illustrate, via a computational example, how CNNs are trained and used in practice to solve a specific class of problems.

Over the last decade, empirical mode decomposition (EMD) has developed into a versatile tool for adaptive, scale-based modal decomposition. EMD has proven to be capable of decomposing multivariate signals with cross-channel mode alignment. However, the algorithms for envelope identification in multivariate EMD come with a computational burden rendering it unsuitable for the large computational demands of multidimensional signal processing. The current work introduces an alternative approach to multivariate EMD, and by combining it with existing fast and adaptive algorithms, paves the way for performing multivariate EMD on multidimensional signals.

Fourier Mellin SOFT (FMS) as a novel method for global registration of 3D data is presented. It determines the seven degrees of freedom (7-DoF) transformation, i.e., the 6-DoF rigid motion parameters plus 1-DoF scale, between two scans, i.e., two noisy, only partially overlapping views on objects or scenes. It is based on a sequence of the 3D Fourier transform, the Mellin transform and the SO(3) Fourier transform. This combination represents a non-trivial complete 3D extension of the well known Fourier-Mellin registration for 2D images. It is accordingly based on decoupling rotation and scale from translation. First, rotation—which is the main challenge for the extension to 3D data - is tackled with a SO(3) Fourier Transform (SOFT) based on Spherical Harmonics. In a second step, scale is determined via a 3D Mellin transform. Finally, translation is calculated by Phase-Matching. Experiments are presented with simulated data sets for ground truth comparisons and with real world data including object recognition and localization in Magnetic Resonance Tomography (MRT) data, registration of 2.5D RGBD scans from a Microsoft Kinect with a scale-free 3D model generated by Multi-View Vision, and 3D mapping by registration of a sequence of consecutive scans from a low-cost actuated Laser Range Finder. The results show that the method is fast and that it can robustly handle partial overlap, interfering structures, and noise. It is also shown that the method is a very interesting option for 6-DoF registration, i.e., when scale is known.

Compressive sensing (CS) of high-order data such as hyperspectral images, medical imaging, video sequences, and multi-sensor networks is certainly a hot issue after the emergence of tensor decomposition. Actually, the reconstruction accuracy with current algorithms is not ideal in some cases of noise. In this paper, we propose a new method that can recover noisy 3-D images from a reduced set of compressive measurements. First, multi-way compressive measurements are performed using Gaussian random matrices. Second, the mapping relationship between the variance of noise and the reconstruction threshold is found. Finally, the original images are recovered through reconstruction of pseudo inverse based on threshold selection. We experimentally demonstrate that the proposed method outperforms other similar methods in both reconstruction accuracy (within a range of the compression ratios and different variances of noise) and processing speed.

It is hard to imagine what the world would look like without the modern technologies using digital signal processing. The developments in this technical field provide an opportunity for building technical devices that implement mathematical methods unattainable by analog technology. Many modern technical devices work with two-dimensional (2-D) signals in a process called digital image processing, and 2-D digital finite impulse response (FIR) filters are basic technical tools in image processing. FIR filters are extensively used in digital television, radio astronomy, radio location, biomedicine, and so on.

Sensing and imaging systems are under increasing pressure to accommodate ever-larger and higher-dimensional data sets; ever-faster capture, sampling, and processing rates; ever-lower power consumption; ever-smaller form factor; and new sensing modalities. These needs have motivated the development of new approaches to signal acquisition and processing. We provide an introduction to the field of compressive sensing (CS), which has stimulated a rethinking of sensor and signal processing system design. In CS, analog signals are digitized and processed not via uniform sampling but via measurements using more general, even random, test functions. In contrast to conventional wisdom, the new theory asserts that one can combine “sub-Nyquist rate sampling” with large-scale optimization for efficient and accurate signal acquisition when the signal has a sparse structure. Particular topics addressed include signal sparsity, randomized sampling, optimization-based signal recovery, and perspectives on applications to seismic data acquisition and processing.

The Fourier transform is widely used to diagnose induction motor faults through the monitoring of fault signatures from measured signals such as stator currents. For a good frequency resolution, Fourier transform needs a long signal acquisition time that increases the probability of speed fluctuations which, leads to fault signatures variations. In addition, limited acquisition time and acquired points generate unwanted sidelobes leakage phenomenon, caused by step frequency resolution. In signal processing, the use of window functions allows the avoidance of this phenomenon with the cost of losing a part of signal information. In this paper, the authors propose a new method for the diagnosis of induction motor broken bar fault based on sliding window discrete Fourier transform and the effect of sidelobes of sideband frequencies on the fundamental component amplitude of stator current. The main advantage of the proposed method is that one can detect the amplitude of the fault indicator frequency in vicinity of the fundamental one in shorter time and with good precision even if the motor turns at no-load when compared to used methods, as fast Fourier transform, zoom fast Fourier transform, multiple signal classification, and zoom multiple signal classification. The simulation and experimental results validate the effectiveness of the proposed method.

Fault detection in induction motors (IM) has been studied during the past decades due to the role that these electric machines play in industry. Regular monitoring is performed on IM to diagnose their operating condition using vibration and stator current analysis. The acquired signal is then processed to extract the characteristic parameters of the fault. The fast Fourier transform (FFT) is used for this task, but it has intrinsic limitations like sensitivity to low signal-to-noise ratio, overlapping of closely-located spectral components, nonstationary signals, and spectral leakage. These limitations have been studied to improve the spectrum estimation, but spectral leakage has not received enough attention, even when its effects can be significant. This paper introduces multirate signal processing techniques that improve the FFT-based methods by reducing spectral leakage with fractional resampling. The methodology is applied to experimental signals to show the improvement of the FFT-based methods for detecting faults in IM.

The main motivation behind compressive sensing is to reduce the sampling rate at the input of a digital signal processing system. However, if for processing the sensed signal one requires to reconstruct the corresponding Nyquist samples, then the data rate will be again high in the processing stages of the overall system. Therefore, it is preferred that the desired processing task is done directly on the compressive measurements, without the need for the reconstruction of the Nyquist samples. This paper addresses the case in which the processing task is "detection" (the existence) of a sparse signal in additive white Gaussian noise, with applications e.g. in radar systems. Moreover, we will propose two estimators for estimating the degree of sparsity of the detected signal. We will show that one of the estimators attains the Cramer-Rao lower bound of the problem. HighlightsSome new descriptions for the detector and estimator have been presented.The equations with respect to ź2 have been now written with respect to p in the whole paper.The Cramer-Rao lower bound (CRLB) for the proposed estimator, which is biased, has been computed.

Sampling plays a critical role in remote sensing and signal analysis. In conventional sampling theory, the signal is sampled at a uniform rate at a minimum of twice the signal bandwidth. However, in many multichannel systems such as analog-to-digital converters, synthetic aperture radar (SAR), and synthetic aperture sonar (SAS), it requires that multidimensional signals or digital images be reconstructed from their recurrent samples, and the signals may not be bandlimited in the traditional Fourier domain. In this paper, a reconstruction algorithm for two-dimensional (2D) recurrently sampled signals is proposed in the fractional Fourier domain. This algorithm can handle the situations where the signal is nonbandlimited, and it is extended to the case of undersampling, where the traditional reconstruction algorithms might fail. The algorithm is based on the nonuniform fractional spectrum, and a method to speed up the computation of the nonuniform fractional spectrum is introduced. Reconstruction from recurrent samples in the case of undersampling is illustrated using numerical examples, and an application to multichannel SAR imaging is included to illustrate these results. HighlightsA reconstruction algorithm for two-dimensional (2D) recurrently sampled signals is proposed in fractional Fourier domain.The proposed algorithm is extended to the case of undersampling, which makes it outstanding of the traditional algorithms in the Fourier domain.An effective algorithm to speed up the computations is proposed.

Analytic envelope is the most prevalent definition of envelopes of real-valued signals. However, analytic signals are not adopted by some envelope detectors in application. This paper investigates the envelopes of real-valued signals from a signal processing perspective. We show that the upper and lower envelopes of signals can be obtained by signal reconstruction after extrema sampling on signals. We prove that extrema sampling is a sub-Nyquist sampling. We then conclude that the envelopes of real-valued signals contain two parts, some low-frequency components of the original signal and some new components generated by sub-Nyquist extrema samplings. Some examples are presented to compare with the analytic envelope of signals.

The majority of signals encountered in real applications, such as radar, sonar, speech, and communications, are often characterized by time-varying spectral contents. For this type of signals whose frequency contents evolve with time, signal representation in time or frequency domain alone cannot fully describe its time-varying characteristics. It would be far more useful to describe the signals with the time-frequency representations (TFRs). The TFRs for processing signals with time-varying frequencies can be generally categorized as linear and nonlinear transforms. The widely used linear transform is the short-time Fourier transform (STFT). The nonlinear transforms include the Wigner-Ville distribution (WVD) and various classes of quadratic time-frequency transforms. During the studies of various signal processing methods, it is found that the local polynomial Fourier transform (LPFT) is an important and effective processing tool for many practical applications, mainly because the LPFT is a linear transform and free from the cross terms that exist in the WVD. Furthermore, the LPFT uses extra parameters to approximate the phase of the signal into a polynomial form to describe time-varying signals with a much better accuracy than the STFT. This thesis focuses on the theoretical analysis of the LPFT, such as its uncertainty principle and SNR analysis, followed by applications to demonstrate its advantages and verify the theoretical analysis of the LPFT. Moreover, the reassignment technique is employed to further increase the concentration of the local polynomial periodogram (LPP), which is the square of the LPFT. DOCTOR OF PHILOSOPHY (EEE)

Multimedia contents are inherently sensitive signals that must be protected when processed in untrusted environments. The field of Secure Signal Processing addresses this challenge by developing methods which enable operating with sensitive signals in a privacy-conscious way. Recently, we introduced a hard lattice problem called m-RLWE (multivariate Ring Learning with Errors) which gives support to efficient encrypted processing of multidimensional signals. Afterwards, Bootland et al. presented an attack to m-RLWE that reduces the security of the underlying scheme from a lattice with dimension \prod_in_i to \max\n_i\ _i . Our work introduces a new pre-/post-coding block that addresses this attack and achieves the efficient results of our initial approach while basing its security directly on RLWE with dimension \prod_in_i, hence preserving the security and efficiency originally claimed. Additionally, this work provides a detailed comparison between a conventional use of RLWE, m-RLWE and our new pre-/post-coding procedure, which we denote "packed''-RLWE. Finally, we discuss a set of encrypted signal processing applications which clearly benefit from the proposed framework, either alone or in a combination of baseline RLWE, m-RLWE and "packed''-RLWE.

Due to the existing relationship between microstructural properties and magnetic ones of the ferromagnetic materials, the application potential of the magnetic Barkhausen noise (BN) method to non-destructive testing is constantly growing. However, the stochastic nature of the Barkhausen effect requires the use of advanced signal processing methods. Recently, the need to apply time-frequency (TF) transformations to the processing of BN signals arose. However, various TF methods have been used in the majority of cases for qualitative signal conditioning and no extensive analysis of TF-based information has been conducted so far. Therefore, in this paper, the wide analysis of BN TF representation was carried out. Considering the properties of TF transformations, the Short-Time Fourier Transform (STFT) was used. A procedure for definition of the envelopes of the TF characteristic was proposed. To verify the quality of extracted features, an analysis was performed on the basis of BN signals acquired during stress loading experiments of steel elements. First, the preliminary experiments were processed for various parameters of the measuring system and calculation procedures. The feature extraction procedure was performed for different modes of TF representations. Finally, the distributions of TF features over the loading stages are presented and their information content was validated using commonly used features derived from time T and frequency F domains.

Remote sensing image plays an irreplaceable role in the defense and civilian sides. Because there are big differences between its image-forming mechanism and visible light image, it is particularly important to study the processing algorithm for the characteristic of this type of graphics. Although the multi-scale geometric analysis algorithm has a good time-frequency characteristics itself and can well solve some multidimensional signal processing problems of the corresponding directions, there are still many shortcomings of the multi-scale geometric transformation generated by theory need to be improved. Some multiscale geometric transformations don’t have shift invariance nature and analytical nature, the direction selectivity are poor and so on, and for the characteristics of remote sensing image, different types of multi-scale geometric transformation has different processing effect. The study is mainly based on the multi-scale geometric transformation which is commonly used, and its main app...

Signal reconstruction from non-uniform samples, especially for non-stationary signals, is an important issue in the area of digital signal processing. As a type of signal processing tool, the fractional Fourier transform has been proved to be effective for solving problems in non-stationary signal processing. For non-stationary discrete-time signals, the reconstruction of uniformly sampled signals from non-uniform samples in the fractional Fourier domain is first derived in this study. Since only finite non-uniform samples are collected in practical applications, for preferable reconstruction, two types of symmetric extensions are considered in the reconstruction to overcome the discontinuity problem that exists in the periodisation of short non-stationary sequences, which is more critical than that of long sequences. In addition, the average signal-to-noise ratio is used to evaluate the performance of the reconstruction with two types of symmetric extensions. Simulations and two applications are given to verify the effectiveness of the proposed reconstruction method.

This tutorial, dedicated both to young professionals and students working with digital signal processing and pattern recognition, introduces three feature extraction approaches based on signal energy, characterising alternative and innovative ways for its use. The proposed theory, smoothly presented, is complemented with numerical examples, source-codes in C/C++ programming language, and applications in a diversity of computational problems, namely, neurophysiological signal processing, speech processing, and image processing. The lack of novelty in current energy-based approaches and the feasibility of a balance among creativity, simplicity, and accuracy constitutes the motivation for this text, which reveals how relevant the concept of signal energy may be, if properly employed.

The digital Taylor-Fourier transform (DTFT) is used to identify low-frequency electromechanical modes in power systems. The identification process is based on the time-frequency analysis of nonlinear signals that arise after a large disturbance. The DTFT creates a signal decomposition, from which mono-component signals are extracted by spectral analysis using a filter bank. This analysis is accomplished through sliding-window data, which is updated each sample, yielding estimates of the reconstructed signal and providing information of its instantaneous damping and frequency. Results demonstrate the applicability of the proposition.

The papers in this special issue are intended to address some of the main research challenges in Graph Signal Processing by presenting a collection of the latest advances in the domain. These papers examine key representation, learning and processing aspects for signals living on graphs and networks, as well as new methods and applications in graph signal processing. Numerous applications rely on the processing of high dimensional data that reside on irregular or otherwise unordered structures that are naturally modeled as networks. The need for new tools to process such data has led to the emergence of the field of graph signal processing, which merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process signals on structures such as graphs. This important new paradigm in signal processing research, coupled with its numerous applications in very different domains, has fueled the rapid development of an inter-disciplinary research community that has been working on theoretical aspects of graph signal processing and applications to diverse problems such as big data analysis, coding and compression of 3D point clouds, biological data processing, and brain network analysis.

Signals and Images: Advances and Results in Speech, Estimation, Compression, Recognition, Filtering, and Processing cohesively combines contributions from field experts to deliver a comprehensive account of the latest developments in signal processing. These experts detail the results of their research related to audio and speech enhancement, acoustic image estimation, video compression, biometric recognition, hyperspectral image analysis, tensor decomposition with applications in communications, adaptive sparse-interpolated filtering, signal processing for power line communications, bio-inspired signal processing, seismic data processing, arithmetic transforms for spectrum computation, particle filtering in cooperative networks, three-dimensional television, and more. This book not only shows how signal processing theory is applied in current and emerging technologies, but also demonstrates how to tackle key problems such as how to enhance speech in the time domain, improve audio quality, and meet the desired electrical consumption target for controlling carbon emissions. Signals and Images: Advances and Results in Speech, Estimation, Compression, Recognition, Filtering, and Processing serves as a guide to the next generation of signal processing solutions for speech and video coding, hearing aid devices, big data processing, smartphones, smart digital communications, acoustic sensors, and beyond.

Signal processing deals with the representation, transformation, and manipulation of signals and the information they contain. Typical examples include extracting the pure signals from a mixture observation (a field commonly known as deconvolution) or particular signal (frequency) components from noisy observations (generally known as filtering). This chapter outlines the basics of signal processing and then introduces the more advanced concepts of time‐frequency and time‐scale representations, as well as emerging fields of compressed sensing and multidimensional signal processing. When moving to multidimensional signal processing, a modern approach is taken from the point of view of statistical (machine) learning. An interesting branch of multidimensional signals and systems analysis is that of spectral analysis on manifolds. The chapter presents the spectral analysis of a mesh by using a combinational graph Laplacian and a geometric mesh Laplacian. Finally, the chapter gives a selected set of illustrative examples to review the discussed basic concepts of signal processing and standard techniques.

In this article, the basic concepts of digital signal processing will be introduced, leading to a mathematical description of a digital signal processor in terms of, first, a difference equation and, second, a z-domain transfer function. In the process, the effects of sampling and quantization will be briefly touched upon. Implementation of a processor by special purpose hardware and discrete Fourier transform technique will be discussed. The Fast Fourier Transform (FFT) will be introduced and several of its applications will be presented, along with the pitfalls and incorrect usage of the technique.‡

We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a corresponding optimization problem. We provide a general solution by using the alternating direction methods of multipliers. We next show how signal inpainting, matrix completion, robust principal component analysis, and anomaly detection all relate to graph signal recovery, and provide corresponding specific solutions and theoretical analysis. Finally, we validate the proposed methods on real-world recovery problems, including online blog classification, bridge condition identification, temperature estimation, recommender system, and expert opinion combination of online blog classification., Comment: To appear on IEEE Transactions on Signal Processing

In many state-of-the-art signal processing techniques, a signal within sliding-window (SW) is assumed stationary for analysing non-stationary signals. Whenever this assumption is violated, inaccuracies increase to the unacceptable levels. A narrow window-width is recommended for limiting the effect of variations within window, however, it results in poor frequency resolution and demands for increased computational resources. This study presents a simple and efficient algorithm to address amplitude-variation in a signal within SW, thus, allowing time resolution of 1-cycle and frequency resolution of 5 Hz (as per IEC Std. 61000-4-7) with improved accuracy and reliability of the fast Fourier transform of the time-varying signal. The proposed algorithm computes and applies necessary corrections to provide accurate estimates of the integer harmonics for the most recent cycle, irrespective of the number of cycles within the SW. The proposed algorithm is computationally efficient and fast, therefore, can be implemented easily either on digital signal processor or field programmable gate arrays hardware platform. The salient features of the proposed algorithm have been validated on variety of simulated and experimental signals, and have been compared with similar existing techniques in practice nowadays.

I benchmarking the well-known Fast Fourier Transforms Library at X86 Xeon E5 2690 v3 system. Fourier transform image processing is an important tool that is used to decompose the image into sine and cosine components. If the input image represented by the equation in the spatial domain, output from the Fourier transform represents the image in the fourier or the frequency domain. Each point represents a particular frequency included in the spatial domain image in the Fourier domain image. Fourier transform is used widely for image analysis, image filtering, image compression and image reconstruction as a wide variety of applications. Fourier transform plays a important role in signal processing, image processing and speech recognition. It has been used in a wide range of sectors. For example, this is often a signal processing, is used in digital signal processing applications, such as voice recognition, image processing. The Discrete Fourier transform is a specific kind of Fourier transform. It maps the sequence over time to sequence over frequencies. If it implemented as a discrete Fourier transform, the time complexity is O (N2). It's actually not a better way to use. Alternatively, the Fast Fourier Transform is possible to easily perform a Discrete Fourier Transform of parallelism with only O (n log n) algorithm. Fast Fourier Transform is widely used in a variety of scientific computing program. If you are using the correct library can improve the performance of the program, without any additional effort. I have a well-known fast Fourier transform library was going to perform a benchmarking on X86 based Intel Xeon E5 2690 systems. In the machine's current Intel Xeon X86 Linux system. I have installed Intel IPP library, FFTW3 Library (West FFT), Kiss -FFT library and the numutils library on Intel X86 Xeon E5 based systems. The benchmark performed at C, and measuring the performance over a range of a transform size. It benchmarks both real and complex transforms in one dimension.

Signal processing can be performed in time domain as well as intransform domain. Frequency domain is perhaps the most widely used domain for transform domain signal processing. In this paper we analyze sequency domain (SD) signal processing as an alternate to the conventional frequency domain signal processing. We perform signal processing in sequency domain using conjugate-symmetric sequency-ordered complex Hadamard transform and compare the results with those of discrete Fourier transform. We observe that in comparison with frequency spectrum, spectral energy of sequency spectrum is spread over the entire spectrum. We performed signal and image denoising in SD and found that our designed SD filters effectively denoise the signals.

The most difficult challenge in developing a high-efficiency embedded image processing system relates to how to execute complicated Digital Signal Processing (DSP) algorithm with embedded processor, especially when processing high-resolution images. A whole system may start to run very slowly because of the large volumes of data being processed and the complexity of the algorithm, rendering it unable to achieve real-time processing. Executing motion detection in low-resolution image was already proved to be able to reduce the loading of data manipulation and to be able to help filter out noise and fake motion. However, smoothing filter pointed out in the work will affect the quality of image. Although the LL-band signal of a 2D Discrete Wavelet Transform (DWT) domain can retain the main part of the energy and information of the original image, a complex algorithm is more suitable for the application of a low-pass filter. Symmetric Mask-based DWT (SMDWT) has the advantage of reduced complexity, regular signal coding, and independent subband coding processing. In this paper, we use a Particle Swarm Optimization (PSO) approach to automatically evolve the multiplierless 2D SMDWT filters hardware architecture. The architecture employs only shift-and-addition operations to replace the complex floating-point multiplication and division operations. It can use shift-and-add based SMDWT filter to decompose a low-resolution image and do real-time image processing system design with low-resolution image processing technique.

In this paper, Analyzed the multi-channel signal processing algorithms for digital-transponder. To analyze suitable multi-channel signal processing algorithms, compare algorithms about four criteria. Four criteria are as follows, perfect reconstruction, interference rejection, resource usage and power consumption. Analysis for each algorithm in accordance with these four criteria. then propose the multi-channel signal processing algorithms for digital satellite communication system.

International audience; In this paper, we introduce a novel direction finding (DF) algorithm for a multi-scale sensor-array, that is, an array presenting multiple scales of spatial invariance. We show that the collected data can be represented as a Candecomp/Parafac (CP) model, for which we analyze the identifiability properties. A two-stage algorithm for direction-of-arrival (DOA) estimation with such an array is also proposed. This approach generalizes the results given in \cite{SidiSPT0800} to an array that presents an arbitrary number of spatial invariances. We illustrate, on two particular array geometries, that our method outperforms, in some difficult scenarios, the ESPRIT-based approach introduced Wong and Zoltowski in 1998, the ESPRIT-MUSIC of Zoltowski and Wong and the Tensor-ESPRIT. Moreover, we show that the single-snapshot case and the fully cross-correlated sources case can be handled by our method without any spatial smoothing procedure, provided that the array includes at least three scale-levels.

International audience; Distance functions are at the core of important data analysis and processing tools, e.g., PCA, classification, vector median filter, and mathematical morphology. Despite its key role, a distance function is often used without careful consideration of its underlying assumptions and mathematical construction. With the objective of identifying a suitable distance function for hyperspectral images so as to maintain the accuracy of hyperspectral image processing results, we compare existing distance functions and define a suitable set of selection criteria. Bearing in mind that the selection of distance functions is highly related to the actual definition of the spectrum, we also classify the existing distance functions based on how they inherently define a spectrum. Theoretical constraints and behavior, as well as numerical tests are proposed for the evaluation of distance functions. With regards to the evaluation criteria, Euclidean distance of cumulative spectrum (ECS) was found to be the most suitable distance function.