Signal Processing and the Design of Microarray Time-Series Experiments

Data Analysis and Signal Processing in Chromatography

State-of-the-art data analysis tools have to deal with high-dimensional data. Fortunately, the inherent dimensionality of data is often much smaller, as it has an internal structure limiting its degrees of freedom. In most cases, this structure can be approximated using a graph, i.e, a set of nodes connected by edges. Based on this idea, graphs have been largely used in semi-supervised and unsupervised learning. The canonical assumption when incorporating a graph prior is to assume that the signal is smooth with respect to the graph, i.e, that connected pieces of data have similar values. Nevertheless, this hypothesis is insufficient to characterize more complex relations between the data and its structure, the graph. To this end, the field of Graph Signal Processing (GSP) extends the graph smoothness hypothesis to a more general assumption. Its key idea is to think of the signal as a sum of harmonic modes, which are obtained from the eigen-decomposition of the Laplacian, an operator representing the second order derivative. Thus, the essence of GSP resides in the Fourier transform defined by the projection on the Laplacian eigenvectors basis, which allows us to filter graph signals. However, GSP suffers from a counterintuitive irregularity. Contrarily to the classical Fourier basis, the graph Laplacian eigenvectors are not spreading uniformly on the vertex set and can be highly concentrated in a region of the graph. This non-uniformity results in a lack of any intuitive translation operator and consequently poses challenges to generalize some of the classical signal processing theory, e.g., stationarity, uncertainty principles, or sampling. In this thesis, we answer these difficulties by accepting that each node is unique and should be treated specially according to its surrounding structure. This is achieved using an operator called localization that shifts a kernel defined in the spectral domain around a specific node while adapting to the local graph structure. In the first part of the thesis, we focus on harmonic analysis in GSP. We start by making use of the norm of localized kernels to capture the spectral local features of the graph vertices. To illustrate the relevance of this analysis we then introduce structural clustering, an algorithm that groups nodes according to the role they play in the graph. Then, we bound the vertex-frequency concentration of graph filter banks atoms. Because of the irregular structure of graphs, we construct a local uncertainty principle that is, again, driven by the norm of a localized kernel. In the second part of the thesis, we tackle GSP problems from a machine learning perspective. We use the localization operator to extend the notion of stationarity to graph signals. It consists of a graph signal probabilistic framework allowing us to optimally solve inverse problems. Finally, we show how the graph total variation can be used in semi-supervised learning and prove its consistency with respect to the underlying graph manifold.

Chapter 7 - Fourier Analysis in Communications and Filtering

One of the basic components of Industry 4.0 is the design of a flexible manufacturing system (FMS), which involves the choice of parameters to optimize its performance. Discrete event simulation (DES) models allow the user to understand the operation of dynamic and stochastic system performance and to support FMS diagnostics and design. In combination with DES models, optimization methods are often used to search for the optimal designs, which, above all, involve more than one objective function to be optimized simultaneously. These methods are called the multi-objective simulation–optimization (MOSO) method. Numerous MOSO methods have been developed in the literature, which spawned many proposed MOSO methods classifications. However, the performance of these methods is not guaranteed because there is an absence of comparative studies. Moreover, previous classifications have been focused on general MOSO methods and rarely related to the specific area of manufacturing design. For this reason, a new conceptual classification of MOSO used in FMS design is proposed. After that, four MOSO methods are selected, according to this classification, and compared through a detailed case study related to the FMS design problem. All of these methods studied are based on Design of Experiments (DoE). Two of them are metamodel-based approaches that integrate Goal Programming (GP) and Desirability Function (DF), respectively. The other two methods are not metamodel-based approaches, which integrate Gray Relational Analysis (GRA) and the VIKOR method, respectively. The comparative results show that the GP and VIKOR methods can result in better optimization than DF and GRA methods. Thus, the use of the simulation metamodel cannot prove its superiority in all situations.

As a result of a successful case study, we advance a methodology for combining design of experiments (DOE) and cumulative score (Cuscore) charts to control and monitor an industrial process subject to a feedback control scheme. We use DOE to screen out the most important variable from a larger set of variables. We use the critical variable found in the DOE phase as a compensating factor in a feedback controller. We derive the proper Cuscore statistic that will identify spike signals in a dynamic system that is subject to feedback control. We then apply this Cuscore statistic to the output error from the control scheme. We illustrate the effectiveness of this process improvement methodology using an industrial case study where we identify and eliminate a recurring output quality problem in a pleating and gluing manufacturing operation.

This is the proceedings of theworkshop on recent developments in ergodic theory and dynamical systemson March 2011and March 2012 at the University of North Carolina at Chapel Hill. Thearticles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval exchange transformations, continued fractions, return times averages, Furstenberg Fractals, fractal geometry of non-uniformly hyperbolic horseshoes, convergence along the sequence of squares, adic and horocycle flows, and topological flows. These contributions illustrate the connections between ergodic theory and dynamical systems, number theory, harmonic analysis, probability, andalgebra. Two surveys are included which give a nice introduction for interested young or senior researcher to some active research areas. Overall this volume provides a very useful blend of techniques and methods as well as directions of research on general convergence phenomena in ergodic theory and dynamical systems.

Introducing some classes of stable systems without any smooth Lyapunov functions

Fourier analysis is one of the most important concepts when you apply physical ideas to engineering issues. This book provides a comprehensive understanding of Fourier transform and spectral analysis in optics, image processing, and signal processing. Written by a world renowned author, this book looks to unify the readers understanding of principles of optics, information processing and measurement. This book describes optical imaging systems through a linear system theory. The book also provides an easy understanding of Fourier transform and system theory in optics. It also provides background of optical measurement and signal processing. Finally, the author also provides a systematic approach to learning many signal processing techniques in optics. The book is intended for researchers, industry professionals, and graduate level students in optics and information processing.

Analyzing the frequency components of the time-varying signals to extract their frequency values and time allocation is required in some applications, i.e.; filter design in signal processing, optics, acoustics and other applications. There are Potential tools have been used for that purpose like Wigner transform, Wavelet transforms, short-time Fourier transform, and fractional Wavelet transform. In this paper, a Novel method is proposed for the time-limited signal to estimate both the frequency component value and its midpoint(mean) time by using the continuous fractional Fourier transform, the proposed method is based on the rotation property of the continuous fractional Fourier transform for function (signal) in the time-frequency plane. Two main applications are discussed. The first is the frequency estimation and its time location for a signal that consists of low frequency time-limited signal in addition to two separable high-frequency components; the other is the time and frequency value estimation of low frequency time-limited signal and two shared additive high-frequency components, simulation verifies the validity of the proposed method, besides the importance of the continuous fractional Fourier transform as a valuable tool in engineering applications like signal processing, and optics. Also, there are many actual Engineering components based on Fourier Analysis like Electrical relay. Its practical applications are expected to grow significantly.

Various applications in digital systems require the involvement of concepts from signal processing and filtering. These specific problems often need the linear dynamic systems to have a transfer function that can specify the behavioural characteristics of the system. When operating in the digital domain, such functions can effectively be used to approximate the same characteristics over the frequency range of importance as any given continuous-time transfer function. In the case with uniform sampling, linear systems theory can directly provide an answer to determine the frequency response. However, when the element of randomness is added to the sample rate of the discrete controller, the common analysis technique of substituting z=ejw will not give the correct result. This paper therefore places an emphasis on the Fourier analysis and highlights a technique to compute the magnitude and phase of a non-uniform rate transfer function at various frequencies in the time domain.

This paper deals with the problem of asymptotically estimating amplitude, frequency and phase of a sinusoidal signal by adopting the theory of invariant relations proposed in analytical mechanics [8] and further investigated in [9], [10] (see also [11]). The problem of frequency, amplitude and phase estimation of a sinusoidal signal has attracted a remarkable research attention in the past and current literature. The reasons of this interest rely on several engineering applications where an effective and robust solution to this problem is crucial. To mention few, it is worth mentioning problems of harmonic disturbance compensation in automatic control, design of phase-looked loop circuits in telecommunication, adaptive filtering in signal processing, etc. In principle, the method of least squares, Fourier analysis, Laplace transform provide a potential solution to the corresponding problems. However, these methods may not be suitable, for example, for control algorithms with real-time data processing. The goal of this paper is to suggest a further contribution to this task by showing how to solve the problem at hand through the observer’s theory. The method of invariant relations is used for the asymptotically observation scheme design. This aproach is based on dynamical extension of original system and construct of appropriate invariant relations, from which the unknowns variables can be expressed as a functions of the known quantities on the trajectories of extended system. The final synthesis is carried out from the condition of obtaining asymptotic estimates of unknown parameters. It is shown that an asymptotic estimate of the unknown states can be obtained by rendering attractive an appropriately selected invariant manifold in the extended state space. The asymptotic convergence of the estimates of the sought phase vector components to their true value is proved. The simulation results demonstrate the effectiveness of the proposed method of solving the state observation problem of the harmonic oscillator. It should be noted that a more general approach, which forms an appropriate method for solving observation problems for nonlinear dynamical systems due to the synthesis of invariant manifold, was proposed as a modification of the I\&I method (Input and Invariance) of stabilization of nonlinear systems in [12, 13].

Sensory neurobiological analysis of neuropeptide modulation of meal size

Field Programmable Gate Arrays (FPGAs) provide flexible computational architectures that are ideal for digital signal processing (DSP). With support of a NIH/NIDCD SBIR grant, we are developing an open FPGA platform for the speech, hearing, and acoustics research communities. The advantage of using FPGAs in a computational platform over conventional CPU approaches is the ability to implement low-latency high-performance signal processing with deterministic latencies. The hardware portion of the platform includes an audio codec and an Intel System-on-Chip (SoC) FPGA that contains ARM CPUs alongside the computational fabric that allows custom data plane designs. Development uses Mathwork’s Simulink that allows exploration and simulation of signal processing algorithms. Once a Simulink model has been developed to implement audio processing in either the time domain or frequency domain, VHDL code can be generated that implements the desired signal processing. The VHDL code is then implemented in the FPGA computational fabric where the FPGA functions as a real-time signal processor. We are currently soliciting ideas/feedback from the speech, hearing, and acoustic communities as to what features they would like to see in the next iteration of the open FPGA-based computational platform. [NIH/NIDCD R44DC015443: www.openspeechtools.com]

A retrospective on 60 years of approximation theory and associated fields

Wavelet analysis is considered a state-of-the-art technique in signal processing; it transforms the signal into a scale-time representation (scalogram) with high resolution, preserving the temporal characteristics of the signal. In the present study, an overview of Fourier analysis, short-time Fourier analysis, and wavelet analysis are given, and the differences between them are addressed. To demonstrate the importance of wavelet analysis in the field of coastal engineering and other related fields, a summary of the recent literature concerning its applications is given first, and then wavelet analysis is used to analyze the complex phenomenon of wave growth due to a sudden change in the wind conditions. This study shows that the temporal characteristics of the time series of wind speed and significant wave height can be explored qualitatively by using the complex Morlet wavelet analysis. The results reveal that the waves are responding immediately to the sudden change in wind conditions.