Frequency-response-shaped LMS adaptive filter

A new LMS algorithm is introduced for improved performance when a sinusoidal input signal is corrupted by correlated noise. The algorithm is based on shaping the frequency response of the transversal filter. This shaping is performed on-line by the inclusion of an additional term similar to the leakage factor in the adaptation equation of leaky LMS. This new term, which involves the multiplication of the filter coefficient vector by a matrix, is calculated in an efficient manner using the FFT. The proposed adaptive filter is shown analytically to converge in the mean and mean-square sense. The filter is also analyzed in the steady state in order to show the frequency-response-shaping capability. Simulation results illustrate that the performance of the frequency-response-shaped LMS (FRS-LMS) algorithm is very effective even for highly correlated noise.     

Optimal feedforward controller design for periodic inputs

This article presents an optimal design methodology for feedforward controllers that face periodic reference/disturbance inputs. The feedforward controller is parametrised as a finite impulse response filter, and its parameters are computed to minimise the worst-case tracking error in the presence of uncertainty on the input period and the plant model. Numerical results indicate that for nonminimum-phase systems exploiting the periodic input characteristics in the feedforward controller design is worthwhile, and reveal the superiority of the developed design methodology with respect to current design approaches when period-time and/or plant uncertainty is present.     

Response properties of an integrate-and-fire model that receives subthreshold inputs

A computational technique is described for calculation of the interspike interval and poststimulus time histograms for the responses of an integrate-and-fire model to arbitrary inputs. The effects of the model parameters on the response statistics were studied systematically. Specifically, the probability distribution of the membrane potential was calculated as a function of time, and the mean interspike interval and PST histogram were calculated for arbitrary inputs. For stationary inputs, the regularity of the output was studied in detail for various model parameters. For nonstationary inputs, the effects of the model parameters on the output synchronization index were explored. The results show that enhanced synchronization in response to low-frequency stimuli required a large number (n > 25) of weak inputs. Irregular responses and a linear input-output rate relationship required strong (but subthreshold) inputs with a small time constant. A model cell with mixed-amplitude synaptic inputs can respond to stationary inputs irregularly and have enhanced synchronization to nonstationary inputs that are phase-locked to low-frequency inputs. Both of these response properties have been reported for some cells in the ventral cochlear nucleus in the auditory brainstem.     

易于硬件实现滤除ECG信号运动干扰的变步长LMS算法

针对移动心电(ECG)信号监测系统中运动干扰难以滤除的问题,提出了一种易于硬件实现的数字自适应变步长最小均方(LMS)算法.通过简化步长因子与输入信号的关系,减少了权值更新系统的运算量;分析传统LMS算法收敛性不稳定的问题,结合迭代次数优化步长因子,提高了算法的收敛性能.对比传统LMS算法,所提算法在运算量增加微小的情况下,收敛性能大幅提升,信噪比(SNR)增加大于14dB.仿真结果表明:算法在心电信号进行实时硬件集成滤除运动干扰方面具有运算量小,滤波效果好等优点.     

Using Bayes' rule to model multisensory enhancement in the superior colliculus

The deep layers of the superior colliculus (SC) integrate multisensory inputs and initiate an orienting response toward the source of stimulation (target). Multisensory enhancement, which occurs in the deep SC, is the augmentation of a neural response to sensory input of one modality by input of another modality. Multisensory enhancement appears to underlie the behavioral observation that an animal is more likely to orient toward weak stimuli if a stimulus of one modality is paired with a stimulus of another modality. Yet not all deep SC neurons are multisensory. Those that are exhibit the property of inverse effectiveness: combinations of weaker unimodal responses produce larger amounts of enhancement. We show that these neurophysiological findings support the hypothesis that deep SC neurons use their sensory inputs to compute the probability that a target is present. We model multimodal sensory inputs to the deep SC as random variables and cast the computation function in terms of Bayes' rule. Our analysis suggests that multisensory deep SC neurons are those that combine unimodal inputs that would be more uncertain by themselves. It also suggests that inverse effectiveness results because the increase in target probability due to the integration of multisensory inputs is larger when the unimodal responses are weaker.     

基于LMS算法自适应噪声抵消器的分析研究

自适应信号处理的理论和技术已经成为人们常用的语音去噪技术,而Matlab为其提供了更为方便快捷的方法来对语音信号进行消噪处理。通过介绍自适应滤波器原理,在对自适应滤波器相关理论研究的基础上,重点研究了LMS自适应滤波算法,并对LMS自适应算法进行了分析,用Matlab对其进行了仿真和实现。     

Modified matched filter for cloud clutter suppression

The least-mean-square (LMS) filter has been developed as an alternative to the classical matched filter (MF) to address the clutter-spectrum issue. However, the output of the MF and the LMS processes is dependent on the scene energy and marginally dependent on the filter signal shape. An approach referred to as the modified matched filter (MMF) is presented. The MMF is a product of the LMS filter and a nonlinear operator known as the inverse Euclidean distance. The nonlinear operator modifies the LMS filter to improve its sensitivity to signal shape. A comparison indicates the relative merit of including shape detection in the LMS clutter-suppression process. Infrared cloud scenes from the background measurements and analysis program (BMAP) were used to demonstrate the relative clutter-suppression performance for both the LMS and the MMF processes. A performance metric is developed to measure cloud clutter suppression quantitatively     

Using an adapted,task-level technology acceptance model to explain why instructors in higher education intend to use some learning management system tools more than others

Instructors in higher education perform some instructional tasks much more often using a learning management system (LMS) tool than other tasks. In studies that aim to explain these differences, the Technology Acceptance Model (TAM) perspective is missing. In this study, an adapted, task-level TAM questionnaire was used to measure task importance, task performance, LMS usefulness, LMS ease of use, and intention to use an LMS for 18 different instructional tasks among 180 instructors at a Dutch research university. The results show that low intention to use an LMS can be explained by (1) low task importance or performance, and/or (2) low LMS usefulness, and/or (3) low LMS ease of use level. The LMS tools and tasks within each of the three groups were not related substantively. This raises a question regarding whether an instructor's LMS intention level can best be explained by the combination of a specific tool, a specific instructional task, and a specific user interface.     

Synchronization of the neural response to noisy periodic synaptic input.

The timing information contained in the response of a neuron to noisy periodic synaptic input is analyzed for the leaky integrate-and-fire neural model. We address the question of the relationship between the timing of the synaptic inputs and the output spikes. This requires an analysis of the interspike interval distribution of the output spikes, which is obtained in the gaussian approximation. The conditional output spike density in response to noisy periodic input is evaluated as a function of the initial phase of the inputs. This enables the phase transition matrix to be calculated, which relates the phase at which the output spike is generated to the initial phase of the inputs. The interspike interval histogram and the period histogram for the neural response to ongoing periodic input are then evaluated by using the leading eigenvector of this phase transition matrix. The synchronization index of the output spikes is found to increase sharply as the inputs become synchronized. This enhancement of synchronization is most pronounced for large numbers of inputs and lower frequencies of modulation and also for rates of input near the critical input rate. However, the mutual information between the input phase of the stimulus and the timing of output spikes is found to decrease at low input rates as the number of inputs increases. The results show close agreement with those obtained from numerical simulations for large numbers of inputs.     

Lyapunov characterization of forced oscillations

This paper develops a Lyapunov approach to the analysis of input-output characteristics for systems under the excitation of a class of oscillatory inputs. Apart from sinusoidal signals, the class of oscillatory inputs include multi-tone signals and periodic signals which can be described as the output of an autonomous system. The Lyapunov approach is developed for linear systems, homogeneous systems (differential inclusions) and nonlinear systems (differential inclusions), respectively. In particular, it is established that the steady-state gain can be arbitrarily closely characterized with Lyapunov functions if the output response converges exponentially to the steady-state. Other output measures that will be characterized include the peak of the transient response and the convergence rate. Tools based on linear matrix inequalities (LMIs) are developed for the numerical analysis of linear differential inclusions (LDIs). This paper's results can be readily applied to the evaluation of frequency responses of general nonlinear and uncertain systems by restricting the inputs to sinusoidal signals. Guided by the numerical result for a second order LDI, an interesting phenomenon is observed that the peak of the frequency response can be strictly larger than the L₂ gain.     

Inferring input nonlinearities in neural encoding models

We describe a class of models that predict how the instantaneous firing rate of a neuron depends on a dynamic stimulus. The models utilize a learnt pointwise nonlinear transform of the stimulus, followed by a linear filter that acts on the sequence of transformed inputs. In one case, the nonlinear transform is the same at all filter lag-times. Thus, this "input nonlinearity" converts the initial numerical representation of stimulus value to a new representation that provides optimal input to the subsequent linear model. We describe algorithms that estimate both the input nonlinearity and the linear weights simultaneously; and present techniques to regularise and quantify uncertainty in the estimates. In a second approach, the model is generalized to allow a different nonlinear transform of the stimulus value at each lag-time. Although more general, this model is algorithmically more straightforward to fit. However, it has many more degrees of freedom than the first approach, thus requiring more data for accurate estimation. We test the feasibility of these methods on synthetic data, and on responses from a neuron in rodent barrel cortex. The models are shown to predict responses to novel data accurately, and to recover several important neuronal response properties.     

On convergence properties of piecewise affine systems

In this paper convergence properties of piecewise affine (PWA) systems are studied. In general, a system is called convergent if all its solutions converge to some bounded globally asymptotically stable steady-state solution. The notions of exponential, uniform and quadratic convergence are introduced and studied. It is shown that for non-linear systems with discontinuous right-hand sides, quadratic convergence, i.e., convergence with a quadratic Lyapunov function, implies exponential convergence. For PWA systems with continuous right-hand sides it is shown that quadratic convergence is equivalent to the existence of a common quadratic Lyapunov function for the linear parts of the system dynamics in every mode. For discontinuous bimodal PWA systems it is proved that quadratic convergence is equivalent to the requirements that the system has some special structure and that certain passivity-like condition is satisfied. For a general multimodal PWA system these conditions become sufficient for quadratic convergence. An example illustrating the application of the obtained results to a mechanical system with a one-sided restoring characteristic, which is equivalent to an electric circuit with a switching capacitor, is provided. The obtained results facilitate bifurcation analysis of PWA systems excited by periodic inputs, substantiate numerical methods for computing the corresponding periodic responses and help in controller design for PWA systems.     

Computational noise effects on adaptive filter algorithms

Finite word length arithmetic roundoff noise in adaptive filter algorithms results in statistical variations in the filter weight vector about the infinite precision arithmetic weight vector. These roundoff errors may be modeled as a statistically non stationary driving noise affecting weight mean and covariance convergence. Mean and covariance expressions and bounds are desired for word lengths in fixed-point arithmetic by making use of multiplication roundoff error models. The adaptive filter algorithms consist of the LMS algorithm, the Widrow-Hoff LMS algorithm, pilot-vector algorithm and clipped vector algorithm. All of these algorithms can be implemented on-line and real-time. However, only the behavior of the LMS algorithm is reported here. The implementation of the adaptive filter algorithms in finite word length arithmetic is most evident in minicomputer, microprocessor, and dedicated digital signal processors for on-line real-time signal identification and parameter estimation in many disciplines. Radar signal processing, adaptive beam forming, acoustic signal identification, communication channel enhancement have a definite need for advanced filtering concepts. Our adaptive algorithms are typically employed in these filter configurations. These filters can also be employed in phase distortion equalizers. A particular advantage of these filters is that they can be trained to equalize a variety of distortions. Should a particular distortion scenario change in time, the filters can be made to easily adapt to the new problem.     

LMS自适应信道估计算法及仿真

提出一种基于连续导频的LMS自适应信道估计算法，在一个符号内进行ⅢS自适应滤波，经多次迭代得到信道估计值，然后根据信道变化速度再对其进行多符号平均。接收系统通过Simulink实现，并通过编写S函数仿真LMS自适应信道估计算法，系统动态仿真结果显示此方法可明显提高信道估计的准确度和接收机性能。     

On Natural Continua of Periodic Solutions of the Systems with Hysteresis

Theorems on the existence of continua of periodic solutions for systems with hysteretic nonlinearities of the type of Preisah models are suggested. It is found that in the general situation, the standard criteria for existence of at least one periodic solution, which rest on the use of prior upper-bound estimates of the norm of periodic solutions and the Leray–Schauder method, ensure the existence of a one-parameter continuum of periodic solutions to these systems. The proofs are based on the use of new classes of operators that describe periodic responses of hysteretic nonlinearities to periodic inputs.     

基于谱减和LMS的自适应语音增强

针对宽带噪声背景下的语音增强问题,将短时语音视为非平稳或宽平稳信号,基于谱减法和自适应滤波的最小均方（LMS）算法,提出了一种FIR型自适应滤波算法（SSLMS）：用减谱法由短时噪声观测语音估计期望信号,作为滤波器输出信号的参考信号;用滤波器的输出与参考信号的差值为误差信号,用LMS算法求得滤波器权系数修正量,并修正滤波器。权系数最速下降调整中,采用了归一化LMS、符号LMS、块LMS技术,以简化保证权系数收敛的步长选择、减少权系数修正的运算量,从而提高自适应速度。对不同的语音在各种信噪比下仿真实验,并与改进的谱减法比较,结果表明,该法增强效果优于谱减法;在信噪比为3 dB时该法的增强效果仍然令人满意。     

Active control of vibration using a neural network

Feedforward control of sound and vibration using a neural network-based control system is considered, with the aim being to derive an architecture/algorithm combination which is capable of supplanting the commonly used finite impulse response filter/filtered-x least mean square (LMS) linear arrangement for certain nonlinear problems. An adaptive algorithm is derived which enables stable adaptation of the neural controller for this purpose, while providing the capacity to maintain causality within the control scheme. The algorithm is shown to be simply a generalization of the linear filtered-x LMS algorithm. Experiments are undertaken which demonstrate the utility of the proposed arrangement, showing that it performs as well as a linear control system for a linear control problem and better for a nonlinear control problem. The experiments also lead to the conclusion that more work is required to improve the predictability and consistency of the performance before the neural network controller becomes a practical alternative to the current linear feedforward systems.     

Improving Robustness Filter Bandwidth in Repetitive Control by Considering Model Mismatch

Repetitive control (RC) is used to track and reject periodic signals by including a model of a periodic signal in the feedback path. The performance of RC can be improved by including an inverse plant response filter, but due to modeling uncertainty at high frequencies, a low‐pass robustness filter is also required to limit the bandwidth of the signal model and ensure stability. The design of robustness filters is presently ad‐hoc, which may result in excessively conservative performance. This article proposes a new automatic method for designing the robustness filter based on convex optimization and an uncertainty model. Experimental results on a nanopositioning system demonstrate that the proposed method outperforms the traditional brick‐wall filter approach.     

Necessary and sufficient conditions for stability of LMS

Guo and Ljung (1995) established some general results on exponential stability of random linear equations, which can be applied directly to the performance analysis of a wide class of adaptive algorithms, including the basic LMS ones, without requiring stationarity, independency, and boundedness assumptions of the system signals. The current paper attempts to give a complete characterization of the exponential stability of the LMS algorithms by providing a necessary and sufficient condition for such a stability in the case of possibly unbounded, nonstationary, and non-φ-mixing signals. The results of this paper can be applied to a very large class of signals, including those generated from, e.g., a Gaussian process via a time-varying linear filter. As an application, several novel and extended results on convergence and the tracking performance of LMS are derived under various assumptions. Neither stationarity nor Markov-chain assumptions are necessarily required in the paper     

Almost-sure convergence of adaptive algorithms by projections

A convergence proof is discussed for the normalized least-mean-square (LMS) algorithm for ergodic inputs. The approach is based on interpreting the algorithm as a sequence of relaxed projection operators by which the key contraction property is derived. The proof technique is strongly motivated by physical intuition, and provides additional insight into LMS-type algorithms under ergodic inputs. Embedded in the development is a slight generalization to a random time-varying gain parameter. This allows the incorporation of variations such as the LMS and signed LMS algorithms