Spline Adaptive Filter Research Articles

Active noise cancellation gets a boost: A novel diffusion-based approach in spline adaptive filters

This study addresses the challenge of unwanted noise in signal processing, particularly for applications requiring high-fidelity audio like noise-canceling headphones. Current adaptive filters offer some noise reduction but struggle with specific noise profiles. We propose the enhanced adaptive filter and a distributed learning utilizing a novel diffusion-based framework that leverages spline adaptation. This innovative approach integrates a natural logarithm and a special function called the hyperbolic cosine for improved noise cancellation. Our method achieves superior noise reduction and improved signal quality compared to existing techniques. This research demonstrates the effectiveness of the enhanced adaptive filter, making it ideal for applications demanding pristine audio and well-suited for distributed noise cancellation scenarios.

A Low Computational Complexity Family of Spline NLMS Adaptive Filter Algorithm

This paper presents novel and low computational complexity spline adaptive filtering (SAF) algorithms based on partial coefficients selection and adaption. They are addressed partial update SAF normalized least mean squares (PU-SAF-NLMS) algorithms. The PU-SAF-NLMS equations are established via the steepest gradient descent constraint to the proposed cost function. In the proposed algorithms, the filter coefficients are updated based on periodic, sequential, and selective rules, leading to reduction in computational complexity. Furthermore, the convergence speed of PU-SAF-NLMS algorithms is close to the conventional SAF-NLMS. Moreover, the convergence analysis of algorithms is studied. Ultimately, the performance of the presented algorithms is appraised through several experimental results.

Sigmoid distance metric-based spline adaptive filters for nonlinear adaptive noise cancellation

This article devises a spline adaptive filter (SAF) algorithm with robustness for nonlinear adaptive noise cancellation (NANC), called the SAF-SDM, which is built on a distance-based metric with a sigmoid kernel. The presented SAF-SDM delivers insignificant coefficient updates when the system is subjected to remarkable outliers, which leads to low steady-state errors. Additionally, we thoroughly analyze the mean behaviour and mean-square performance of the SAF-SDM at the theoretical level and validate the analysis results using nonlinear system identification (NSI) simulations. To fulfill the higher computational efficiency when a longer linear filter order is selected in the SAF, an improved SAF-SDM is developed through a frequency domain (FD) filtering program, called the FDSAF-SDM. Then, we provide an analysis of the calculation complexity of the two presented algorithms and compare them with those of several similar algorithms. Finally, simulation and experiment results demonstrate the excellence of the presented algorithms in NSI and NANC.

Design of efficient Wiener spline adaptive filter for electrocardiogram signal enrichment

Design of efficient Wiener spline adaptive filter for electrocardiogram signal enrichment

The q-gradient LMS spline adaptive filtering algorithm and its variable step-size variant

In this study, an innovation q-gradient least-mean-square (LMS) spline adaptive filtering (S-AF) algorithm (SAF-qLMS) on the basis of the theory of q-derivative is proposed. The q-calculus confronts the issue of slow convergence by mitigating the over-reliance of LMS-type algorithms on the diffusion of eigenvalues in the input correlation matrix. Compared to conventional derivatives, the SAF-qLMS exploits q-calculus to compute the secant of the cost function, enabling it to take larger steps in the search direction for q>1. Furthermore, for balancing the convergence rate and steady-state error of SAF-qLMS and solving the deficiency of the fixed step-size, the SAF-VqLMS based on variable step-size is further proposed. Finally, the convergence conditions of the SAF-qLMS are discussed. Simulations in a correlated Gaussian input environment confirm the outstanding performance of the proposed algorithms for nonlinear system identification.

Rational b-spline adaptive filter for active noise control of machinary noises

Spline adaptive filter has a different architecture than linear-in-parameter nonlinear filters like Volterra filter. There are various kinds of splines like Bezier spline, B-spline and rational B-spline. Rational B spline has weights associated with control points and hence, provides more flexibility than B-spline to create a curve. This paper presents development of rational b-spline adaptive filter for active noise control. Updating equations to update control points and weights of control points are derived. A simulation study is presented to study performance of proposed rational B-spline adaptive filter to reduce machinary noises. Performance of proposed rational B-spline filter are compared with B-spline filter and Bezier filter for active noise control of experimentally recorded noises of band-saw, CNC machine and compressor

A 2D-LUT Scheme Design for Complex-Valued Spline Adaptive Filter

This brief presents a two dimensional Look-Up-Table (2D-LUT) scheme for complex-valued (CV) spline adaptive filter. The key idea of this structure is to model a complex-valued nonlinear static function by implementing the Carstesian product of two univariate cubic uniform B-spline curves. Therefore, the real and imaginary components of the system complex-valued output can be readily achieved hinging on two different sets of spline control point respectively, each of which is stored in a 2D-LUT separately. In addition, as an extension of the real-valued (RV) sign spline adaptive algorithm, the CV counterpart is also derived to update both the weight coefficients of the linear subsystem and spline control points associated with 2D-LUTs. Simulations on the identification of RF nonlinear power amplifier (PA) show that the proposed scheme outperforms the existing methods in terms of estimation accuracy against impulsive noises, as well as lower computational complexity.

Optimal Design of Hammerstein Cubic Spline Filter for Nonlinear System Modeling Based on Snake Optimizer

This work develops a new class of Hammerstein adaptive filters that contains a memory-less non-linear system followed by a linear adaptive filter, where the non-linear system comprises an adjustable look-up table (LUT) and a spline interpolator. This paper's first effort has been to employ the meta-heuristic algorithm (MHA) to the Hammerstein spline adaptive filter (HSAF), where it concurrently updates the weights of spline control points and linear filter based on the estimation problem. A novel MHA called snake optimiser algorithm (SOA) is used to enhance the assurance of convergence, estimated parameter accuracy and steady-state results. The presented experimental results indorse that the proposed SOA-based HSAF (SOA-HSAF) design exhibits more robust performance in dealing with higher degree non-linear systems under the Gaussian and Non-Gaussian circumstances compared to contemporary design methods like classical, some standard MHAs and other researchers reported techniques. The achieved simulation results are validated using a TMS320C6713 digital signal processor.

Underwater four-quadrant dual-beam circumferential scanning laser fuze using nonlinear adaptive backscatter filter based on pauseable SAF-LMS algorithm

The phenomenon of a target echo peak overlapping with the backscattered echo peak significantly undermines the detection range and precision of underwater laser fuzes. To overcome this issue, we propose a four-quadrant dual-beam circumferential scanning laser fuze to distinguish various interference signals and provide more real-time data for the backscatter filtering algorithm. This enhances the algorithm loading capability of the fuze. In order to address the problem of insufficient filtering capacity in existing linear backscatter filtering algorithms, we develop a nonlinear backscattering adaptive filter based on the spline adaptive filter least mean square (SAF-LMS) algorithm. We also designed an algorithm pause module to retain the original trend of the target echo peak, improving the time discrimination accuracy and anti-interference capability of the fuze. Finally, experiments are conducted with varying signal-to-noise ratios of the original underwater target echo signals. The experimental results show that the average signal-to-noise ratio before and after filtering can be improved by more than 31 dB, with an increase of up to 76% in extreme detection distance.

Spline adaptive filtering algorithm based on different iterative gradients: Performance analysis and comparison

Two novel spline adaptive filtering (SAF) algorithms are proposed by combining different iterative gradient methods, i.e., Adagrad and RMSProp, named SAF-Adagrad and SAF-RMSProp, in this paper. Detailed convergence performance and computational complexity analyses are carried out also. Furthermore, compared with existing SAF algorithms, the influence of step-size and noise types on SAF algorithms are explored for nonlinear system identification under artificial datasets. Numerical results show that the SAF-Adagrad and SAF-RMSProp algorithms have better convergence performance than some existing SAF algorithms (i.e., SAF-SGD, SAF-ARC-MMSGD, and SAF-LHC-MNAG). The analysis results of various measured real datasets also verify this conclusion. Overall, the effectiveness of SAF-Adagrad and SAF-RMSProp are confirmed for the accurate identification of nonlinear systems.

Nonlinear Spline Versoria Prioritization Optimization Adaptive Filter for Alpha-Stable Clutter

The increasing demand for a better quality of service in radar and wireless communications has attracted research on interference suppression. Nonlinear filtering methods based on spline architecture have been widely utilized in signal processing due to their effectiveness against alpha-stable interference. However, existing nonlinear spline adaptive filter algorithms suffer from high steady-state misalignment. To achieve lower steady-state misalignment along with having comparable computational complexity, we propose a nonlinear spline Versoria prioritization optimization adaptive filter (SPOAF-MVC) for alpha-stable clutter in this article. Furthermore, we study the bound on learning rate and computational complexity for the proposed algorithm. Numerical simulations confirm the effectiveness and efficiency of the proposed SPOAF-MVC algorithm for alpha-stable clutter under the Wiener system identification.

Robust Frequency Domain Spline Adaptive Filtering Based on the Half-Quadratic Criterion: Performance Analysis and Applications

Frequency domain spline adaptive filters (FDSAF) have attracted a great deal of attention because of their enhanced computational efficiency. However, their performance will be extremely degraded in practical environments where non-Gaussian phenomena exist. In order to attain good robustness to non-Gaussian noises while ensuring a low computational burden, this paper proposes a frequency domain spline adaptive filtering algorithm based on the half-quadratic criterion (HQC), named FDSAF-HQC. Further, to offer a theoretical foundation for the proposed FDSAF-HQC, a detailed performance analysis based on the principle of energy conservation is conducted and then validated by simulations. Moreover, the computational complexity of FDSAF-HQC is evaluated and compared with other similar algorithms. Simulation results of nonlinear system identification corroborate the outstanding performance of the proposed FDSAF-HQC, i.e., better robustness and computational efficiency. The superiority of the proposed FDSAF-HQC is also supported by practical applications of echo cancellation and biological signal denoising.

Nonlinear Spline Adaptive Filters based on a Low Rank Approximation

Nonlinear spline adaptive filters are a class of adaptive filters for modelling nonlinear systems. To improve the convergence performance of existing nonlinear spline adaptive filters (SAFs), in this paper, we propose a low rank approximation for different SAF models by incorporating the technique of nearest Kronecker product decomposition. We consider the Wiener and Hammerstein SAF models for developing the proposed algorithms, and simulation studies carried out show that improved convergence and tracking performance can be achieved compared to traditional SAFs.

Performance Analysis of Orthogonal Gradient Sign Algorithm Using Spline-based Hammerstein Model for Smart Application

This paper presents a spline-based Hammerstein model for adaptive filtering based on a sign algorithm with the normalised orthogonal gradient algorithm. Spline-based Hammerstein architecture consists of an interpolation spline-based adaptive lookup table in the part of nonlinear filter and an adaptive finite impulse response filter used in the part of linear filter. Hammerstein spline adaptive filter (HSAF) is a nonlinear filter for the nonlinear systems among the advantages in the low computational cost and high performance. An adaptive lookup table and spline control points are determined and derived with the orthogonal gradient-based mechanism. Performance analysis in terms of convergence properties and mean square analysis based on the mean square error (MSE) constraint are proven by using the Taylor series expansion of the estimation error in the form of the excess MSE. Experimental results indicate the robust performance of the proposed algorithm can provide the better performance than the other models based on the conventional least mean square Hammerstein spline adaptive filtering algorithm.

Digital Predistortion of Nonlinear Power Amplifier Based on Improved Spline Adaptive Filtering Method

To improve the modeling accuracy and digital predistortion compensation effect, this paper proposed a kind of polynomial based spline adaptive filter (SAF) power amplifier (PA) behavioral modeling method. The proposed model can solve the shortcomings of the traditional memory polynomial model (MP), such as higher nonlinear order, highly coefficient calculation difficulty, poor hardware stability, low modeling accuracy and poor digital predistortion compensation. Meanwhile, the proposed SAF based model can avoid the pseudo-inversion operation of the matrix when calculating the coefficients through the indirect learning structure, which can improve the compensation effect of digital predistortion. In order to compare the performance of the different models, the modeling processes of original filtering model, MP model and dynamic variation reduction (Dynamic Deviation Reduction, DDR) model based on SAF method (OSAF, MPSAF, DDRSAF) are presented respectively. The proposed models are verified by a class F PA, which are stimulated by a set of measured input and output data of an LTE signal with 20 MHz bandwidth. The measured results shows that compared with the conventional MP model, the proposed DDRSAF model presents the best model performance and improves the modeling accuracy by 6.6dB while maintaining the similar computational complexity, and the ACPR compensation effect increases by 19.58dB and 20.47dB respectively, which have the important significance for practical engineering application.

Diffusion Hammerstein Spline Adaptive Filtering Based on Orthogonal Gradient Adaptive Algorithm

In this paper, we propose a class of nonlinear diffusion filtering based on Hammerstein function with the spline adaptive filter (HSAF) implemented by normalised version of orthogonal gradient adaptive (NOGA) algorithm over the distributed network. Diffusion adaptation algorithm approximates a variable vector with the help of a network of agents using a joint optimisation on the sum of cost function. A HSAF comprises of memoryless function during learning by interpolating polynomials with respect to the linear filter. We derive a diffusion adaptation framework on HSAF motivated from NOGA algorithm; called DHSAF-NOGA. There are two types of adaptive diffusion strategies with the combine-then-adapt (CTA) algorithm and the adapt-then-combine (ATC) algorithm that are considered and implemented by DHSAF-NOGA algorithm. The network stability and performance over mean square error networks is derived. Experiment results depict that proposed CTA-DHSAF-NOGA and ATC-DHSAF-NOGA algorithms can learn robustly underlying the nonlinear Hammerstein model compared with a non-cooperative solution and existing techniques.

Frequency domain maximum correntropy criterion spline adaptive filtering

A filtering algorithm based on frequency domain spline type, frequency domain spline adaptive filters (FDSAF), effectively reducing the computational complexity of the filter. However, the FDSAF algorithm is unable to suppress non-Gaussian impulsive noises. To suppression non-Gaussian impulsive noises along with having comparable operation time, a maximum correntropy criterion (MCC) based frequency domain spline adaptive filter called frequency domain maximum correntropy criterion spline adaptive filter (FDSAF-MCC) is developed in this paper. Further, the bound on learning rate for convergence of the proposed algorithm is also studied. And through experimental simulations verify the effectiveness of the proposed algorithm in suppressing non-Gaussian impulsive noises. Compared with the existing frequency domain spline adaptive filter, the proposed algorithm has better performance.

An improved spline adaptive filter for nonlinear system identification under impulsive noise environment

Aiming at the negative influence of impulse noise in conventional spline adaptive filtering (SAF) algorithm in nonlinear system identification, an improved spline adaptive filtering algorithm is proposed. The algorithm mainly improves on two aspects. First, the cost function is constructed by using the hyperbolic tangent function. When the independent variable fluctuates sharply, the cost function will only approach a finite value, which improves the robustness of the filter in an impulse noise environment. In addition, a pre-filtering observation strategy is proposed to further improve the convergence speed of the algorithm and reduce the steady-state error caused by the iterative process in the system. Through the analysis of the amplitude of the noise in the time domain and the frequency domain, the update rule of the weight is determined. The simulation results show that it has better performance than the existing SAF algorithm.

Analysis of Normalized Orthogonal Gradient Adaptive Algorithm Based on Spline Adaptive Filtering for Smart Communication Technology

This paper presents a general theoretical framework of spline adaptive filtering based on a normalized version of orthogonal gradient adaptive algorithm. A nonlinear spline adaptive filter normally consists of a linear combination with a memory-less function and a spline function for adaptive approach. We explain how the adaptive linear filter and spline control points are derived in a straightforward iterative gradient-based method. In order to improve the convergence characteristics, the normalized version of orthogonal gradient adaptive algorithm is introduced by the orthogonal projection along with the gradient adaptive algorithm. In addition, a simple form of adaptation algorithm is introduced how to obtain a lower bound on the excess mean square error (MSE) in a theoretical basis. Convergence and stability analysis based on the MSE criterion are proven in terms of the excess MSE. Simulation results reveal that the proposed algorithm achieves more robustness compared with the conventional spline adaptive filtering algorithm.

Pipelined nonlinear spline filter for speech prediction

In this paper, a new pipelined nonlinear spline adaptive filter (PNSF) is presented for the speech prediction application. The proposed architecture is essentially an improved pipelined cascade model, where each module consists of a FIR filter followed by a spline activation function. Based on minimum mean square error cost and stochastic gradient method, the on-line learning adaptive algorithms for updating the nonlinear and linear weights are derived. We analyze the selection range of the learning rate involved in the learning algorithms to ensure the convergence of the algorithms. Simulations are carried out to evaluate the performance of the PNSF on nonlinear system identification and speech prediction. Experimental results show that the PNSF provides better performance compared to the spline adaptive filter (SAF), joint process filter using pipelined second-order Volterra filter (JPPSOV) and pipelined neural IIR (PNIIR) models.