A stochastic gradient adaptive filter with gradient adaptive stepsize

The step size of this adaptive filter is changed according to a gradient descent algorithm designed to reduce the squared estimation error during each iteration. An approximate analysis of the performance of the adaptive filter when its inputs are zero mean, white, and Gaussian noise and the set of optimal coefficients are time varying according to a random-walk model is presented. The algorithm has very good convergence speed and low steady-state misadjustment. The tracking performance of these algorithms in nonstationary environments is relatively insensitive to the choice of the parameters of the adaptive filter and is very close to the best possible performance of the least mean square (LMS) algorithm for a large range of values of the step size of the adaptation algorithm. Several simulation examples demonstrating the good properties of the adaptive filters as well as verifying the analytical results are also presented     

基于FPGA的梯度自适应格型滤波器设计

对于高灵敏度的数字信号的处理需要使用数值特性优良的格型滤波器。利用EDA技术设计了梯度自适应格型滤波器。实验表明更新反射系数的步长应随着模块数的增加逐步减小。对梯度自适应格型滤波器的单独模块采用驰豫超前技术设计,显著提高了FPGA的运行时钟速率。     

A complex adaptive notch filter using modified gradient algorithm

A modified gradient algorithm is developed for improving the convergence speed of a first-order complex adaptive IIR notch filter, which is used for estimating an unknown frequency of a complex sinusoidal signal embedded in white Gaussian noise. The new cost function using new error criterion is presented and analyzed theoretically. The proposed technique can significantly improve the convergence speed as compared with a complex notch filter using plain gradient algorithm. The computer simulations are conducted to demonstrate the validity of the proposed complex adaptive notch filter.     

Minimisation of gradient artefacts in cardiac-MRI-gating using adaptive interference cancellation filter with synthesised reference

A simple and successful method for cardiac-MRI-gating is proposed. The adaptive interference cancellation filter (AICF) is used with a synthesised reference signal to reduce the gradient artefacts caused by the magnetic resonance (MR). The reference signals of the AICF were a combination of the noisy, three-channel ECG signals. In particular, the proposed method is based on a simple experimental setup and does not require any information from amplifiers of the MRI machine, such as shape, amplitude and rise time.     

A multistep size (MSS) frequency domain adaptive filter

A multistep size frequency-domain adaptive filter capable of tracking both stationary and nonstationary signals is proposed. This algorithm makes use of the simple structure of the least mean square error algorithm to update the filter coefficients and process the signal. It then proceeds further by incorporating a set of three step sizes and a knowledge-based strategy to select the best set of filter coefficients and the optimum step size iteratively. The main advantage of the MSS algorithm over the conventional LMS algorithm is that better performance is achieved without the knowledge of the input signal characteristics, such as signal power, degree of nonstationarity, signal-to-noise ratio, and stability bounds. Experimentally, the MSS algorithm is tested under various signal environments. The transient characteristics of the step sizes are found to be in agreement with previous theoretical studies of nonstationary characteristics of the LMS algorithm. In order to reduce the complexity, the conventional frequency-domain block LMS structure is also modified so that the MSS algorithm can be embedded more efficiently by exploiting the block structure     

Steady-state analysis of a complex adaptive notch filter using modified gradient algorithm

Based on power spectral density (PSD) analytical technique, mean square error (MSE) (or variance) of the frequency estimate of a first-order complex adaptive IIR notch filter (ANF) using modified complex plain gradient (MCPG) algorithm is investigated in this paper. The steady-state expression for MSE is derived in closed form. A quantitative analysis for the estimation MSE has been carried out. It has been revealed that the MSE of frequency estimate is independent of an input frequency of a complex sinusoid. In addition, computer simulations are treated to corroborate the theoretical analysis and the relationships between MSE and system parameters are shown.     

Theoretical analysis of adaptive optics system based on stochastic parallel gradient descent algorithm

The adaptive optics (AO) technology without a wave-front sensor is simple and has more application fields than conventional AO technologies. The theory basis of the AO system based on stochastic parallel gradient descent (SPGD) from the convergence, the stability, and the averaged convergence rate is analyzed, where SPGD is used to control the AO system. The results show that the AO system based on SPGD can obtain good convergence and stability, and the fast convergence rate, which is in inverse proportion to $ \sqrt n $ \sqrt n (n is the number of control parameters).     

Averaged stochastic gradient algorithms for adaptive blindmultiuser detection in DS/CDMA systems

In this paper, we present a blind adaptive gradient (BAG) algorithm for code-aided suppression of multiple-access interference (MAI) and narrow-band interference (NBI) in direct-sequence/code-division multiple-access (DS/CDMA) systems. This BAG algorithm is based on the concept of accelerating the convergence of a stochastic gradient algorithm by averaging. This ingenious concept of averaging was invented by Polyak and Juditsky (1992)-this paper examines its application to blind multiuser detection and NBI suppression in DS/CDMA systems. We prove that BAG has identical convergence and tracking properties to recursive least squares (LMS) but has a computational cost similar to the least mean squares (LMS) algorithm-i.e., an order of magnitude lower computational cost than RLS. Simulations are used to compare our averaged gradient algorithm with the blind LMS and LMS schemes     

Improved adaptive joint probabilistic data association filter formultiple targets angles tracking

The joint probabilistic data association filter that uses a modified algorithm for update time selection is presented. Simulation results illustrate the effectiveness, in terms of data association, of the proposed algorithm for multiple targets angles tracking     

Analysis of the dynamics of a memoryless nonlinear gradient IIR adaptive notch filter

A nonlinear dynamical model of a memoryless nonlinear gradient IIR adaptive notch filter for estimating the frequency of a noisy sinusoid is derived. The model is verified through simulations, where simulated responses of the estimated frequency are compared with the responses obtained from the model with good agreement. Convergence properties of the filter are studied using the model, and maximum step sizes and initial frequency ranges for convergence are determined. The performance of the adaptive filter in tracking a time-varying signal frequency is also examined.     

Statistical performance analysis of a fast stochastic gradient for constrained adaptive time delay estimation

An efficient bi-state stochastic gradient is proposed for spontaneous constrained time delay estimation. The quantized stochastic gradient is an approximation of the polarity of the instantaneous delay estimation error. It is adjusted in such a way that it has a much higher probability to move in the correct direction at each iteration so as to enable a speed-up in the delay estimate to converge to global minimum in steady state. The performance of the delay estimator is evaluated statistically and an analytical solution for its convergence behavior is established. It is demonstrated that the proposed algorithm has at least a two-fold improvement in convergence speed when compared with the conventional approach, and this is verified by extensive simulation results.     

Complex fuzzy adaptive filter with LMS algorithm

A fuzzy adaptive filter is constructed from a set of fuzzy IF-THEN rules that change adaptively to minimize some criterion function as new information becomes available. This paper generalizes the fuzzy adaptive filter based on least mean squares (LMS) to include complex parameters and complex signals. The fuzzy filter as adaptive equalizer is applied to quadrature amplitude modulation (QAM) digital communication with linear complex channel characteristics     

改进的基于白化滤波器的降晰函数尺寸估计方法

给出了一种改进的降晰函数尺寸估计方法,它能为图像盲复原提供重要的先验信息,增强复原结果的可靠性.该算法首先由AR模型导出白化滤波器,然后对降质图像白化后的结果进行两种操作,以保证算法在低信噪比下的可行性:一是利用AR模型误差在边缘区域与平滑区域的差异,通过边缘提取与膨胀操作实现有效区域的快速提取;二是对有效区域通过平滑滤波进行噪声项的有效抑制.最后,对滤波后的有效区域进行相关值计算,依据取得最小值时的位移与降晰函数尺寸之间的关系估计降晰函数的尺寸.该方法经仿真实验验证:在低信噪比时,较改进前的方法能给出可靠的尺寸估计.     

Noise adaptive rational filter

A new rational filter (RF), called the noise adaptive rational filter (NARF), is developed for removing non-impulsive noise, such as Gaussian noise concerned in this paper. The optimal NARF, in the least mean-square (LMS) error sense, is first derived for the one-dimensional signal, followed by its extension to the two-dimensional signal through a separable approach for image denoising. Due to the feasibility issue encountered in the derived optimal closed form, a feasible (thus, sub-optimal) NARF is then proposed, which exploits noise variance (or power) to adapt to signal transitions. The vector NARF is also proposed for color image denoising. Extensive simulation results show that our proposed NARF outperforms the RF on both objective evaluation in peak signal-to-noise ratio (PSNR) measurement and subjective evaluation through visual quality assessment. Furthermore, how to exploit the proposed NARF for denoising a noisy image corrupted by a mixture of impulse noise and non-impulsive noise using a two-stage cascading approach is also discussed with some simulation results.     

A monolithic adaptive filter

Reports a monolithic adaptive filter which has been realized using purely analog sampled-data MOS and CCD techniques. The filter implements a full Widrow least mean-squares algorithm over 65 data points. Central to this design is a novel, compact analog multiplier/accumulator circuit, which is presented in detail. The 65-point adaptive filter, which is cascadable, dissipates 200 mW from a 15 V supply, and operates at sample rates up to 100 kHz.     

Robust Huber adaptive filter

Classical filtering methods are not optimal when the statistics of the signals violate the underlying assumptions behind the theoretical development. Most of the classical filtering theory like least-squares filtering assumes Gaussianity as its underlying distribution. We present a new adaptive filter that is optimal in the presence of Gaussian noise and robust to outliers. This novel robust adaptive filter minimizes the Huber objective function. An estimator based on the Huber objective function behaves as an L₁ norm estimator for large residual errors and as an L₂ norm estimator for small residual errors. Simulation results show the improved performance of the Huber adaptive filter (configured as a line enhancer) over various nonlinear filters in the presence of impulsive noise and Gaussian noise     

An adaptive resonant filter

A solid-state adaptive (analog storage) device with stable electrical characteristics is described and demonstrated. The device is a resonant bandpass electronic filter with adaptable voltage gain; that is, the voltage gain-frequency transfer characteristic can be "set" to different values of attenuation by the application of an adapt signal and will retain that "setting" after the adapt signal has been removed. Ferroelectric materials are used as the dielectric in a filter structure composed of two capacitors bonded together so that resonant mechanical vibrations established in one (the input resonator) are coupled to the other (the output resonator). Converse and direct piezoelectric effects generate the mechanical vibrations and the output voltages, respectively. Ferroelectric effects in either capacitor provide the analog storage capabilities. The acoustical coupling mechanism employed in the device design results in electrically stable device characteristics. Previous ferroelectric adaptive devices used unstable field effect coupling mechanisms which led to unacceptable device performance. Experimental adaptive resonant filters fabricated with ceramic lead zirconate-lead titanate material compositions are discussed. These filters have electronic Q values near 100 at resonant frequencies in the range 10²to 10⁷Hz. The voltage gain-frequency characteristic has a maximum value at resonance of about 0 to +10 dB. Application of a voltage adapt pulse (100 to 300 volts) of low energy (mJ) to either side of the filter can adapt the entire gain characteristic by any value between 0 and about -60 dB within an arbitrary switching time (limited to a practical range of roughly 10⁺³to 10^-4seconds) as determined by the pulse amplitude. Voltage gain settings are electrically stable and can be reproduced by the same or an equivalent sequence of adapting pulses.     

Improved adaptive observer with optimal convergence

A simple technique for simultaneous parameter identification and state estimation of linear discrete systems is presented. The gradient method is used for identification and the global stability of the scheme is guaranteed by the use of Lyapunov's method. The optimal adaptive gains are also considered for more rapid convergence.     

Improved filter sharpening

We propose a natural extension to Kaiser-Hamming (1977) filter sharpening methods to allow for a piecewise linear desired amplitude change function (ACF). The primary advantages of the proposed ACF over piecewise constant ACFs is that we obtain better control of selective improvement (or degradation) in either the passband or stopband or both, and we are not restricted to applying our methods to filters with piecewise constant pass and stopbands, since linear segments of slope 1 can be used to retain existing filter performance in either passband or stopband. The proposed ACF approximating polynomial (AP) is easy to compute, may be constrained to have simple (or integer) coefficients, and may be expressed as the AP of Kaiser and Hamming plus a correction polynomial. We also provide applications for motivation     

A family of adaptive filter algorithms with decorrelatingproperties

Although the normalized least mean square (NLMS) algorithm is robust, it suffers from low convergence speed if driven by highly correlated input signals. One method presented to overcome this problem is the Ozeki/Umeda (1984) affine projection (AP) algorithm. The algorithm applies update directions that are orthogonal to the last P input vectors and thus allows decorrelation of an AR(P) input process, speeding up the convergence. This article presents a simple approach to show this property, which furthermore leads to the construction of new algorithms that can handle other kinds of correlations such as MA and ARMA processes. A statistical analysis is presented for this family of algorithms. Similar to the AP algorithm, these algorithms also suffer a possible increase in the noise energy caused by their pre-whitening filters