Finite Impulse Response Model Research Articles

A Compact Pi Network for Reducing Bit Error Rate in Dispersive FIR Channel Noise Model

During signal transmission, the combined effect of the transmitter filter, the transmission medium, and additive white Gaussian noise (AWGN) are included in the channel which distort and add noise to the signal. This causes the well defined signal constellation to spread causing errors in bit detection. A compact pi neural network with minimum number of nodes is proposed. The replacement of summation at each node by multiplication results in more powerful mapping. The resultant pi network is tested on six different channels. Keywords—Additive white Gaussian noise, digital communication system, multiplicative neuron, Pi neural network. I. INTRODUCTION HE most basic elements of a communication system is a source of signal, a channel which introduces distortion as well as noise and a receiver with a means of detecting errors caused by noise. As higher-level modulation becomes more desirable to cope with the need for high-speed data transmission, nonlinear distortion becomes a major factor, which limits the performance of communication systems. Additive Gaussian noise can disturb the digitally modulated signal during transmission. Additive superimposed noise normally has a constant power density and a Gaussian amplitude distribution throughout the bandwidth of a channel. The source in the communication system model generates a 4- QAM complex valued symbol set. The combined effect of the transmitter filter, the transmission medium, and additive white Gaussian noise (AWGN) are included in the channel. A widely used channel model is a finite impulse response (FIR) model whose output at time instant k is given by (1):

Identification of Mechanical Systems through Kautz Filter

This paper presents a novelty approach to estimate the impulse response function (IRF) in lightly damped structures by using classical covariance method. The contribution of the present paper is to employ a Kautz filter to reduce the number of terms in the identification process of a finite impulse response (FIR) model. The Kautz filter is an orthogonal function that includes complex pole pair. So, the method incorporates a priori knowledge into the process that is essential to reach better results and to minimize the number of coefficients in the FIR model. For this reason, the present approach can be classified as a kind of “grey-box” methodology. The numerical and experimental applications of the method confirmed that by considering a priori parametric information the problem can be determined more easily. Moreover, the procedure proposed increased the convergence speed, and, as a consequence the consuming computational cost is lower.

A Two-Stage Method for Identification of Dual-Rate Systems with Fast Input and Very Slow Output

A dual-rate system with fast input and very slow output is very common in the chemical process industry. To identify its original fast single-rate model based on the output error method, a two-stage method combining techniques for dealing with initialization and local minimum problems is proposed in this paper. In its first stage, a finite impulse response (FIR) model is developed directly from the original dual-rate sampled data using the combined least-squares criterion and Newton−Raphson (N−R) method. In the second stage, a single-and-fast-rate output error model is developed on the basis of the original fast input signal and the derived slow rate model output. Besides the simulation examples, the method is also applied to develop a composition observer for an industrial distillation column.

Consistent estimation of real NMP zeros in stable LTI systems of arbitrary complexity

In this contribution we show that under certain conditions it is possible to estimate a non-minimum phase zero consistently using a very simple 2 parameter finite impulse response model, for arbitrarily complex finite dimensional stable linear time invariant systems.

MIMO Equalization With State-Space Channel Models

State-space models are proposed to represent multiple-input multiple-output (MIMO) frequency-selective wireless channels with the motivation of better model approximation and more robust channel equalization performance when the order of the channel model is lower that of the true channel. We develop a simple framework under which the equalizers for state-space channel models can be designed using the existing methods for designing equalizers for finite impulse response (FIR) models. In particular, a MIMO minimum mean-squared error decision feedback equalizer is developed for state-space models. When only estimates of the channel are available to the receiver, the equalization performance is affected by the channel estimation accuracy. Because reduced-order state-space models can provide lower <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> channel estimation error than reduced-length FIR models, state-space based equalizers typically exhibit significantly smaller symbol error rate than FIR-based ones. Thus, state-space channel models can be a more robust choice than FIR models in the presence of model order selection error. Numerical simulation also shows that adaptive state-space based receivers have slower but comparable convergence rates compared to FIR-based adaptive equalizers.

Synthesis of run-to-run repetitive control methods using finite impulse response models

This paper presents linear quadratic (LQ) repetitive control (RC) methods for processes represented by a conventional FIR model and a circulant FIR model. The latter, which represents a FIR system under the assumption of a cyclic steady state, is named as such as its input–output map is represented by a circulant matrix. Using the complete frequency resolving property of a circulant matrix, a special tuning method for the LQ weights is proposed. Performance of the proposed method is investigated through numerical examples.

Hankel-Norm Approximation of IIR by FIR Models: A Constructive Method

This paper presents a constructive method for (sub)optimal finite-impulse response (FIR) approximation of infinite-impulse response (IIR) models. The method minimizes the Hankel norm of the approximation error by using an explicit solution to the norm-preserved dilation problem. It has advantages over the existing methods in that it is a unified method for both single-input single-output and multiple-input multiple-output systems which allows direct tradeoff between the least-squares and Chebyshev error criteria by using a single tuning parameter, and that the approximation algorithm is constructive and only involves algebraic manipulations rather than iteration and convex optimization procedures. The lower and upper bounds on the l <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and Chebyshev norms of the approximation error are derived and are related to the tuning parameter. The problem of approximating noncausal IIR models by causal FIR models is also formulated and solved. The effectiveness and properties of the proposed algorithms are demonstrated by examples.

Different Dynamics of Performance and Brain Activation in the Time Course of Perceptual Learning

Perceptual learning is regarded as a manifestation of experience-dependent plasticity in the sensory systems, yet the underlying neural mechanisms remain unclear. We measured the dynamics of performance on a visual task and brain activation in the human primary visual cortex (V1) across the time course of perceptual learning. Within the first few weeks of training, brain activation in a V1 subregion corresponding to the trained visual field quadrant and task performance both increased. However, while performance levels then saturated and were maintained at a constant level, brain activation in the corresponding areas decreased to the level observed before training. These findings indicate that there are distinct temporal phases in the time course of perceptual learning, related to differential dynamics of BOLD activity in visual cortex.

An adaptive model predictive control configuration for production–inventory systems

In this paper, an adaptive model predictive control (MPC) configuration is proposed for the identification and control of production–inventory systems. The time-varying dynamic behavior of the production process is approximated by an adaptive Finite Impulse Response (FIR) model. The well-known recursive least-squares (RLS) method is used for the online identification of the model coefficients. The adapted model along with a smoothed estimation of the future customer demand are used to predict inventory levels over the optimization horizon. The efficiency of the proposed scheme is evaluated regarding its capability to eliminate the inventory drift. The performance of the method with respect to the bullwhip effect is also considered and studied in the paper. Comparison with non-adaptive control approaches illustrates the advantages of the proposed method.

Parameter estimation error bounds for Hammerstein nonlinear finite impulsive response models

This paper presents a parameter estimation algorithm for a class of Hammerstein nonlinear systems – input nonlinear FIR (finite impulse response) models, and studies in detail the convergence properties of the proposed identification algorithm in the stochastic framework, and derives the upper and lower bounds of the parameter estimation errors (PEE) from the available input–output data. The analysis indicates that the mean square PEE upper and lower bounds of the algorithm approach zero as the data length increases. A simulation example is given.

A Bias-Compensated Identification Approach for Noisy FIR Models

A new bias-compensated least-squares method for identifying finite impulse response (FIR) models whose input and output are affected by additive white noise is proposed. By exploiting the statistical properties of the equation error of the noisy FIR system, an estimate of the input noise variance is obtained and the noise-induced bias is removed. The results obtained by means of Monte Carlo simulations show that the proposed algorithm outperforms other bias-compensated approaches and allows to obtain an estimation accuracy comparable to that of total least-squares without requiring the a priori knowledge of the input-output noise variance ratio.

Structured low-rank approximation and its applications

Fitting data by a bounded complexity linear model is equivalent to low-rank approximation of a matrix constructed from the data. The data matrix being Hankel structured is equivalent to the existence of a linear time-invariant system that fits the data and the rank constraint is related to a bound on the model complexity. In the special case of fitting by a static model, the data matrix and its low-rank approximation are unstructured.We outline applications in system theory (approximate realization, model reduction, output error, and errors-in-variables identification), signal processing (harmonic retrieval, sum-of-damped exponentials, and finite impulse response modeling), and computer algebra (approximate common divisor). Algorithms based on heuristics and local optimization methods are presented. Generalizations of the low-rank approximation problem result from different approximation criteria (e.g., weighted norm) and constraints on the data matrix (e.g., nonnegativity). Related problems are rank minimization and structured pseudospectra.

Parameter identification of multi-input, single-output systems based on FIR models and least squares principle

By means of auxiliary models – finite impulse response (FIR) models, this paper develops an identification algorithm for multi-input, single-output stochastic systems. The basic idea is to estimate the FIR model parameters of each fictitious subsystem (submodel) with the FIR model orders increasing, and to use auxiliary models to predict/estimate the outputs of the submodels, and further to use the Pade approximation method to produce the parameter estimates of submodels. Some simulation results are given.

Modeling low‐frequency fluctuation and hemodynamic response timecourse in event‐related fMRI

Functional magnetic resonance imaging (fMRI) suffers from many problems that make signal estimation difficult. These include variation in the hemodynamic response across voxels and low signal-to-noise ratio (SNR). We evaluate several analysis techniques that address these problems for event-related fMRI. (1) Many fMRI analyses assume a canonical hemodynamic response function, but this assumption may lead to inaccurate data models. By adopting the finite impulse response model, we show that voxel-specific hemodynamic response functions can be estimated directly from the data. (2) There is a large amount of low-frequency noise fluctuation (LFF) in blood oxygenation level dependent (BOLD) time-series data. To compensate for this problem, we use polynomials as regressors for LFF. We show that this technique substantially improves SNR and is more accurate than high-pass filtering of the data. (3) Model overfitting is a problem for the finite impulse response model because of the low SNR of the BOLD response. To reduce overfitting, we estimate a hemodynamic response timecourse for each voxel and incorporate the constraint of time-event separability, the constraint that hemodynamic responses across event types are identical up to a scale factor. We show that this technique substantially improves the accuracy of hemodynamic response estimates and can be computed efficiently. For the analysis techniques we present, we evaluate improvement in modeling accuracy via 10-fold cross-validation.

Software sensors for monitoring of a solid waste composting process

AbstractProcess identification for composting of tobacco solid waste in an aerobic, adiabatic batch reactor was carried out using neural network-based models which utilized the nonlinear finite impulse response and nonlinear autoregressive model with exogenous inputs identification methods. Two soft sensors were developed for the estimation of conversion. The neural networks were trained by the adaptive gradient method using cascade learning. The developed models showed that the neural networks could be applied as intelligent software sensors giving a possibility of continuous process monitoring. The models have a potential to be used for inferential control of composting process in batch reactors.

NONPARAMETRIC METHOD FOR IDENTIFICATION OF MIMO HAMMERSTEIN MODELS

A new nonparametric approach to identify multivariable Hammerstein models is presented in this paper. The linear dynamic subsystem is identified and represented by its finite impulse response (FIR) model, and, the static nonlinearity is identified and represented as an MIMO input-output mapping. By specially designed test signals, the estimation of FIRs for multivariable linear subsystems can be conducted under a SISO framework and can be decoupled from the identification of the static nonlinearity. Due to the nonparametric nature, the representation of MIMO Hammerstein model may not be unique. By making uses of this fact, several parameters can be adjusted to shape the model for achieving engineer's requirement. These above-mentioned representations can be used to obtain an exact process model or an apparent model suitable for control design.

Historical solar variability derived from sunspot areas using a FIR model

We present new historical reconstructions since 1875 of several parameters of solar variability of interest for climate modeling, including spectral solar irradiance at ultraviolet wavelengths and average magnetic field. The reconstructions are based on our Finite Impulse Response (FIR) model, presented in previous work, which establishes the detailed relationship between observed solar variability and sunspots. This model predicts very little long‐term secular trend in the level of solar minimum for any of the reconstructed solar parameters. Cycle‐averaged spectral solar irradiance at ultraviolet and extreme ultraviolet wavelengths increases by about 3% and 20%, respectively, during the first half of the twentieth century. The corresponding cycle‐averaged change in the average magnetic field is about 50%. We estimate that from the Maunder Minimum to the present, the cycle‐averaged increase is about 4% for the irradiance at 200 nm, 30% for the irradiance at 121.6 nm and 100% for the average magnetic field.

Validity and power in hemodynamic response modeling: A comparison study and a new approach

One of the advantages of event-related functional MRI (fMRI) is that it permits estimation of the shape of the hemodynamic response function (HRF) elicited by cognitive events. Although studies to date have focused almost exclusively on the magnitude of evoked HRFs across different tasks, there is growing interest in testing other statistics, such as the time-to-peak and duration of activation as well. Although there are many ways to estimate such parameters, we suggest three criteria for optimal estimation: 1) the relationship between parameter estimates and neural activity must be as transparent as possible; 2) parameter estimates should be independent of one another, so that true differences among conditions in one parameter (e.g., hemodynamic response delay) are not confused for apparent differences in other parameters (e.g., magnitude); and 3) statistical power should be maximized. In this work, we introduce a new modeling technique, based on the superposition of three inverse logit functions (IL), designed to achieve these criteria. In simulations based on real fMRI data, we compare the IL model with several other popular methods, including smooth finite impulse response (FIR) models, the canonical HRF with derivatives, nonlinear fits using a canonical HRF, and a standard canonical model. The IL model achieves the best overall balance between parameter interpretability and power. The FIR model was the next-best choice, with gains in power at some cost to parameter independence. We provide software implementing the IL model.

Enhanced detection-guided NLMS estimation of sparse FIR-modeled signal channels

In various signal-channel-estimation problems, the channel being estimated may be well approximated by a discrete finite impulse response (FIR) model with sparsely separated active or nonzero taps. A common approach to estimating such channels involves a discrete normalized least-mean-square (NLMS) adaptive FIR filter, every tap of which is adapted at each sample interval. Such an approach suffers from slow convergence rates and poor tracking when the required FIR filter is long. Recently, NLMS-based algorithms have been proposed that employ least-squares-based structural detection techniques to exploit possible sparse channel structure and subsequently provide improved estimation performance. However, these algorithms perform poorly when there is a large dynamic range amongst the active taps. In this paper, we propose two modifications to the previous algorithms, which essentially remove this limitation. The modifications also significantly improve the applicability of the detection technique to structurally time varying channels. Importantly, for sparse channels, the computational cost of the newly proposed detection-guided NLMS estimator is only marginally greater than that of the standard NLMS estimator. Simulations demonstrate the favourable performance of the newly proposed algorithm

Least-squares estimation of a class of frequency functions: A finite sample variance expression

A new expression for the variance of scalar frequency functions estimated using the least-squares method is presented. The expression is valid for finite sample size and for a class of model structures, which includes finite impulse response, Laguerre and Kautz models, when the number of estimated parameters coincides with the number of excitation frequencies of the input. The expression gives direct insight into how excitation frequencies and amplitudes affect the accuracy of frequency function estimates. With the help of this expression, a severe sensitivity of the accuracy with respect to the excitation frequencies is exposed. The relevance of the expression when more excitation frequencies are used is also discussed.