Linear Filter

Correlation of generalization measures to classifier performance. In both cases ( equal to 0.5 or 0.95) the classifier performance as measured by the area of the ROC curve or Pfa at Pd equal 0.8, has an opposite correlation as to what would be expected of a useful measure for predicting performance.

Functional link-based neural network models were applied to predict opencast mining machineries noise. The paper analyzes the prediction capabilities of functional link neural network based noise prediction models vis-à-vis existing statistical models. In order to find the actual noise status in opencast mines, some of the popular noise prediction models, for example, ISO-9613-2, CONCAWE, VDI, and ENM, have been applied in mining and allied industries to predict the machineries noise by considering various attenuation factors. Functional link artificial neural network (FLANN), polynomial perceptron network (PPN), and Legendre neural network (LeNN) were used to predict the machinery noise in opencast mines. The case study is based on data collected from an opencast coal mine of Orissa, India. From the present investigations, it could be concluded that the FLANN model give better noise prediction than the PPN and LeNN model.

Computational vision often needs to deal with derivatives of digital images. Such derivatives are not intrinsic properties of digital data; a paradigm is required to make them well-defined. Normally, a linear filtering is applied. This can be formulated in terms of scale-space, functional minimization, or edge detection filters. The main emphasis of this paper is to connect these theories in order to gain insight in their similarities and differences. We take regularization (or functional minimization) as a starting point, and show that it boils down to Gaussian scale-space if we require scale invariance and a semi-group constraint to be satisfied. This regularization implies the minimization of a functional containing terms up to infinite order of differentiation. If the functional is truncated at second order, the Canny-Deriche filter arises.

Massive Multiple Input Multiple Output (MIMO) system has gathered lately a huge interest from researchers and it has been known as a backbone technology for the 5th generation because it can greatly improve the capacity of wireless communication and it can potentially provide energy efficiency and security. Before ensuring the full advantages, massive MIMO system has to overcome many challenges. One of them is to accurate an exact estimation of the Channel Impulse response (CIR) between each transmit-receive antenna pair. The other problem arises when implementing such a system in presence of High Power Amplifiers (HPA) which imposes a nonlinear distortion on the transmitted signals. This paper proposes contributions in three key areas. Firstly, we investigate the nonlinear effects of memoryless HPA, which is modeled using Saleh model, by deriving its Bit Error Rate expression (BER) in massive MIMO Orthogonal Frequency Division Multiplexing (OFDM) system. Secondly, we highlight the necessity of providing the accurate channel characteristics by estimating it using Compressive Sensing (CS) techniques. Moreover, we propose also a CS compensation algorithm based on Orthogonal Matching Pursuit (OMP) to mitigate the nonlinear distortion in the receiver. The proposed CS-based compensation technique has been compared to the Neural Network (NN) pre and post compensation technique and it has shown a good performance not only in terms of BER but also in terms of complexity.

Linear filters are often employed in most signal processing applications. As a matter of fact, they are well understood within a uniform theory of discrete linear systems. However, many physical systems exhibit some nonlinear behaviour, and in certain situations linear filters perform poorly. One case is the problem of acoustic echo cancellation, where the digital filter employed has to identify as close as possible the acoustic echo path that is found to be highly nonlinear. In this situation a better system identification can be achieved by a nonlinear filter. The problem is to find a nonlinear filter structure able to realize a good approximation of the echo path without any significant increase of the computational load. Conventional Volterra filters are well suited for modelling that system but they generally need too many computational resources for a real time implementation. In this paper we consider some low complexity nonlinear filters in order to find out a filter structure able to achieve performances close to those of the Volterra filter, but with a reduced increase of the computational load in comparison to the linear filters commonly employed in commercial acoustic echo cancellers.

Linear filters are often employed in most signal processing applications. As a matter of fact, they are well understood within a uniform theory of discrete linear systems. However, many physical systems exhibit some nonlinear behaviour, and in certain situations linear filters perform poorly. One case is the problem of acoustic echo cancellation, where the digital filter employed has to identify as close as possible the acoustic echo path that is found to be highly nonlinear. In this situation a better system identification can be achieved by a nonlinear filter. The problem is to find a nonlinear filter structure able to realize a good approximation of the echo path without any significant increase of the computational load. Conventional Volterra filters are well suited for modelling that system but they generally need too many computational resources for a real time implementation. In this paper we consider some low complexity nonlinear filters in order to find out a filter structure able to achieve performances close to those of the Volterra filter, but with a reduced increase of the computational load in comparison to the linear filters commonly employed in commercial acoustic echo cancellers.

We examine the influence of camera design on the estimation of the motion and structure of a scene from video data. Every camera captures a subset of the light rays passing though some volume in space. By relating the differential structure of the time varying space of light rays to different known and new camera designs, we can establish a hierarchy of cameras. This hierarchy is based upon the stability and complexity of the computations necessary to estimate structure and motion. At the low end of this hierarchy is the standard planar pinhole camera for which the structure from motion problem is non-linear and ill-posed. At the high end is a camera, which we call the full field of view polydioptric camera, for which the problem is linear and stable. We develop design suggestions for the polydioptric camera, and based upon this new design we propose a linear algorithm for structure-from-motion estimation, which combines differential motion estimation with differential stereo.

Widely linear estimation for complex-valued signal processing is growing in popularity, especially in the cases where the involved signals exhibit non-circular characteristics. In this paper, the extended Wirtinger's calculus in complex Reproducing Kernel Hilbert Spaces (RKHS), presented in [1], is adopted to derive complex kernel-based widely-linear estimation filters. Furthermore, we illuminate several important characteristics of widely linear filters, which, to our knowledge, haven't been considered before. Our results indicate that, in contrast to many cases where the gains from adopting widely linear estimation filters, instead of ordinary linear filters, are rudimentary, for the case of kernel-based widely linear filters significant performance improvements can be obtained.

This paper addresses a new design method of recursive least-squares (RLS) and finite impulse response (FIR) filter, using covariance information, in linear continuous-time stochastic systems. The signal process is observed with additive white noise. It is assumed that the white observation noise is independent of the signal process. The auto-covariance function of the signal is expressed in the semi-degenerate kernel form. The RLS-FIR filter uses the following information: 1. The auto-covariance function of the signal expressed in the semi-degenerate kernel form. 2. The variance of the white observation noise process.

We look at joint regular variation properties of MA(∞) processes of the form X = (X k , k ∈ Z) where X k = ∞ j=0 ψ j Z k-j and the sequence of random variables (Z i , i ∈ Z) are i.i.d. with regularly varying tails. We use the setup of M O -convergence and obtain hidden regular variation properties for X under suitable summabality conditions on the constant coefficents (ψ j : j ≥ 0). Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.

Based on a fluorescence imaging model, the optical filters, such as excitation and emission filters, are determined by linear discriminant analysis. The discriminability is a quadratic Rayleigh quotient of one filter if the other filter is assumed to be constant. The optical filters are optimized alternatingly and iteratively by solving their generalized eigenvalue problems. The proposed method is validated to design a fluorescence imaging system for poultry fecal inspection.

In the classical Kalman-Bucy filter and in the subsequent literature so far, it has been assumed that the initial value of the signal process is independent of both the noise of the signal and of the noise of the observations.The purpose of this paper is to prove a filtering equation for a linear system where the (normally distributed) initial value X 0 of the signal process X t has a given correlation function with the noise (Brownian motion B t ) of the observation process Z t . This situation is of interest in applications to insider trading in finance. We prove a Riccati type equation for the mean square error where Xt is the filtered estimate for X t . Moreover, we establish a stochastic differential equation for Xt based on S(t). Our method is based on an enlargement of filtration technique, which allows us to put the anticipative linear filter problem into the context of a nonanticipative two-dimensional linear filter problem with a correlation between the signal noise and the observation noise.

A real time structural acoustic sensor and associated signal processing is developed and applied to the active control of sound radiated by a simply supported beam. The sensor consists of multiple accelerometers mounted on the structure. An array of FIR filters processes the measured structural information to provide an estimate of the structural wave-number component coupled to acoustic radiation in a prescribed direction. This time domain signal is used as the error information in a feedforward adaptive control approach. The single channel filtered-X LMS algorithm is implemented here. Computer simulations in the discrete time domain demonstrate the ability of the sensor to replace the use of error microphones in the far field. The described sensor represents a significant alternative to the use of distributive structural sensors (for example piezoelectric material) by providing accurate radiation information over a broadband frequency range.

Any linear phase sampling algorithm can be described as a linear filter characterized by its frequency response. In traditional phase sampling interferometry the phase of the frequency response has been ignored because the impulse responses can be made real selecting the correct sample offset. However least squares methods and recursive filters can have a complex frequency response. In this paper, we derive the quadrature equations for a general phase sampling algorithm and describe the role of the filter phase.

Over the past decade, Convolutional Networks (ConvNets) have renewed the perspectives of the research and industrial communities. Although this deep learning technique may be composed of multiple layers, its core operation is the convolution, an important linear filtering process. Easy and fast to implement, convolutions actually play a major role, not only in ConvNets, but in digital image processing and analysis as a whole, being effective for several tasks. However, aside from convolutions, researchers also proposed and developed non-linear filters, such as operators provided by mathematical morphology. Even though these are not so computationally efficient as the linear filters, in general, they are able to capture different patterns and tackle distinct problems when compared to the convolutions. In this paper, we propose a new paradigm for deep networks where convolutions are replaced by non-linear morphological filters. Aside from performing the operation, the proposed Deep Morphological Network (DeepMorphNet) is also able to learn the morphological filters (and consequently the features) based on the input data. While this process raises challenging issues regarding training and actual implementation, the proposed DeepMorphNet proves to be able to extract features and solve problems that traditional architectures with standard convolution filters cannot. INDEX TERMS Convolutional networks, deep learning, deep morphological networks, mathematical morphology.

Over the past decade, Convolutional Networks (ConvNets) have renewed the perspectives of the research and industrial communities. Although this deep learning technique may be composed of multiple layers, its core operation is the convolution, an important linear filtering process. Easy and fast to implement, convolutions actually play a major role, not only in ConvNets, but in digital image processing and analysis as a whole, being effective for several tasks. However, aside from convolutions, researchers also proposed and developed non-linear filters, such as operators provided by mathematical morphology. Even though these are not so computationally efficient as the linear filters, in general, they are able to capture different patterns and tackle distinct problems when compared to the convolutions. In this paper, we propose a new paradigm for deep networks where convolutions are replaced by non-linear morphological filters. Aside from performing the operation, the proposed Deep Morphological Network (DeepMorphNet) is also able to learn the morphological filters (and consequently the features) based on the input data. While this process raises challenging issues regarding training and actual implementation, the proposed DeepMorphNet proves to be able to extract features and solve problems that traditional architectures with standard convolution filters cannot. INDEX TERMS Convolutional networks, deep learning, deep morphological networks, mathematical morphology.

Interpolated and warped digital waveguide mesh algorithms have been developed to overcome the problem caused by direction and frequency-dependence of wave travel speed in digital waveguide mesh simulations. This paper reviews the interpolation methods applicable in the two-dimensional case. The bilinear interpolation technique and two other approaches are briefly recapitulated. The use of 2-D quadratic interpolation results in a mesh structure that is efficiently implemented using only additions and binary shifts. The optimized interpolated 2-D mesh is obtained by choosing the free parameters of the interpolation method so that the difference in wave travel speed in the axial and diagonal directions is minimized. The output signal of any digital waveguide mesh can be processed with a warped FIR filter to reduce the dispersion error at all frequencies. The frequency-warping factor must be optimized individually for each mesh structure. We introduce an extended method called multiwarping, which can be used to further decrease the dispersion error. The frequency range of digital waveguide mesh simulations is also discussed.

In this paper, a new theory of two-degrees-of-freedom (2-DOF)-H ∞ and certainty-equivalent filters is presented. Exact and approximate solutions to the nonlinear H ∞ filtering problem using this class of filters are derived in terms of discrete-time Hamilton-Jacobi-Isaacs equations. The expressions for the filter gains are determined as functions of the filter state and the system's output in contrast to earlier results. Hence, it is shown that coupled with the additional degree-of-freedom, these filters are a substantial improvement over the earlier 1-DOF case. The theory presented is also generalized to n-DOF filters, which bore strong connections to linear infinite-impulse response filters and hence are generalizations of this class of filters to the nonlinear setting. Simulation results are also given to show the usefulness of the new approach.

A nonrecursive structure of 1-D and 2-D FIR lowpass and highpass digital filters is described in the paper. The magnitude sensitivity is small and zero sensitivity can be obtained at particular frequencies in the passbands. The structure is canonical in the sense of the number of multipliers. The reductions of the structure due to the symmetries of the impulse response are applicable as is usual with the linear phase systems. quency is equal to c . c, irrespective of values of the coefficients di in the structure. The filter synthesis with a given transfer function m = -M I = -N can be performed as shown by the structure in Fig. la. At first, the transfer function should be rearranged to the form 1

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Finite-data-record performance and breakdown behaviors are analytically derived for a space-time "blind" rake-receiver algorithm in a previous proposed by Wong, Lok, Lehnert, and Zoltowski (WLLZ) for uplink direct sequence-code division multiple access (DS-CDMA) cellular wireless communications using only single-user-type "conventional" detectors with either short or long spreading sequences. WLLZ is significant because it needs no prior knowledge nor explicit estimation of 1) the fading channel's multipaths' arrival angles/delays/amplitudes/complex-phases, 2) the receiver's nominal or actual (i.e., calibrated) antenna-array manifold, and 3) the other CDMA users' signature spreading-codes. This analysis a) reveals how the multiuser access cellular system's various parameters influence WLLZs "blind" beamformer's output SINR. These herein-derived quantitative relationships are explicit, closed-form, and accurate to within 1/2-2 dB for the examined scenarios if WLLZ does not break down . This analysis also b) explains WLLZ's breakdown, which can occur for channels with large delay-spreads, due to a matrix rank deficiency, explicitly in closed-form and in terms of the fading-channel's delay spread and temporal variability. It also c) proposes a simple algorithmic modification to WLLZ to avert its breakdown.

Absfmct-This paper describes a new approach to the design of multidimensional (M-D) finite-wordlength digital filters with specifications in the frequency and spatial domains. The approach is based on stochastic optimization and extends previous work on finite impulse response (FIR) filters in two ways: by inclusion of spatial constraints and by application to the case of infinite impulse response (IIR) filters. The formulation proposed is based on a multiple-term objective function that, in addition to magnitude constraints, also includes step response, group delay and stability constraints. Our attention to these characteristics stems from the application of such filters to video processing that we are actively pursuing. Since filter coefficients are of finite precision and since the objective function is multivariable, nondifferentiable and likely to have multiple minima, we use simulated annealing for optimization. We show numerous examples of the design of practical filters such as channel and luminancdchrominance separation filters used in the NTSC system. We demonstrate the impact of coefficient precision as well as of group delay and step response constraints on filter parameters.

Simple reaction time (RT) to a sinusoidal grating was analyzed in terms of a linear filter model of the detection process. First, RT contrast functions were determined over a wide range of spatial frequencies and retinal illuminances. Second, calculating the time course of the linear filter's response, theoretical visual latency contrast functions were derived for the same conditions of spatial frequency and retinal illuminance as those in the RT measurements. Comparison of the two functions showed that the contrast dependence of the RT functions was much larger than that of the visual latency functions. The discrepancy between the two functions was satisfactorily described as a power function of the slope ofthe filter's response at threshold level. On the basis of these results, we propose a model of the RT process. According to the model, the RT process is mediated by a cascade that consists of a level detector, which includes a linear filter followed by a threshold device, and a differentiator of the filter's response. Simple reaction time (RT), defined as the interval between stimulus onset and response initiation, has been a useful tool for psychophysical investigation of the human sensory decision process. Suprathreshold temporal properties of the visual system have been examined with measurement ofRT as a function of stimulus parameters such as intensity (Bartlett

Model reference active structural acoustic control is experimentally investigated in this study for physical systems characterized by stationary, narrow-band disturbances in which the acoustic field remains relatively unchanged. The filtered-x version of the multichannel adaptive least-mean-square (LMS) algorithm was implemented on a TMS320C25 digital signal processing board to achieve the desired control approach, and control inputs were generated with piezoelectric actuators. Model reference control provides the designer with a method of replacing acoustic error sensors such as microphones located in the far-field with error sensors such as accelerometers located on the surface of the structure. As opposed to driving the response of the structure to zero at the coordinates of the accelerometers, the response is driven to some predetermined ‘‘reference’’ value corresponding to the desired far-field acoustic directivity pattern. In essence, the uncontrolled structure is adaptively m...