Linear Filter Research Articles

A Robust Algorithm for the Design of Wideband Positive-Slope Linear Group Delay Filters

This article proposes a robust method for the synthesis and design of optimal linear group delay filters with prescribed bandwidth and dispersion properties. The proposed filters are based on a cascade of second-order all-pass filter cells, for which all the parameters are optimized in order to reach the desired wideband linear group delay characteristic with positive slope. Compared to the previously published synthesis method, the proposed approach offers appropriate initialization enabling convergence and aiming for the optimal solution. The method’s convergence and robustness are proved through a 21-cells synthesis, which is the highest number of cascaded cells reported to date, due to the usual convergence problem. Then the electronic feasibility is illustrated through the measurement results of a lumped-elements linear group-delay filter prototype dimensioned with this method. The measured group delay presents a positive slope of 8 ns GHz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> in the frequency range [100–725] MHz. It is, to the best of our knowledge, the highest positive slope reported to date with an electronic implementation (i.e except SAW and waveguide devices).

Improving the robustness of spectral estimation to loud transients with a truncated order statistics filter

Underwater acoustic recordings often include loud transients from human or natural sources. The transients cause a positive bias for Welch's average periodogram spectral estimator when estimating the power spectral density of the background environment. Estimators based on single order statistics (e.g., the sample median) avoid the bias caused by outliers at the cost of a higher variance than the sample mean. Schwock and Abadi (2021) showed that, for exponential random variables, the estimator based on the 80th sample percentile has the lowest variance among any unbiased estimator based on a single order statistics. This work tests a hybrid approach between Welch's and order statistics estimators by performing a weighted sum of the quietest subset of ordered samples of the periodograms. By discarding the loudest samples of the periodogram, the truncated linear order statistics filter (TLOSF) reduces the bias caused by loud transients. By combining multiple order statistics into the estimate, the TLOSF achieves a lower variance than the 80th percentile estimator. The TLOSF reduced the MSE by 1dB compared to Schwock &amp; Abadi's 80th percentile estimator for a mixture combining an exponential distribution with 1% outliers 23 dB above the background. On periodograms of shallow water hydrophone recordings, the TLOSF yielded a lower output power in the frequency bins where both the Welch's and 80th percentile estimators had a positive bias due to loud transients. [Work supported by ONR Code 321US.]

Tens to Hundreds of Mrad/s Fast Polarization Tracking and Demultiplexing Using Angle-Plus-Phase Algorithm in Stokes Space

A fast polarization tracking and demultiplexing algorithm in polarization-division-multiplexing (PDM) systems is proposed and demonstrated. The scheme utilizes two optimizing parameters in Stokes Space, including the polarization angle and the phase information. In addition to its transparency to modulation formats, the angle-plus-phase algorithm (APA) could provide fast convergence up to >100-Mrad/s polarization tracking speed. Compared to common polarization demultiplexing algorithms such as constant modulus algorithm (CMA) and linear Kalman filter (LKF), experimental results show that the polarization tracking capability of the proposed APA algorithm is significantly improved without sacrificing the transmission performance. Specifically, compared to CMA, the tracking speed can be improved from 9-Mrad/s to 160-Mrad/s for PDM quadrature phase shift keying (PDM-QPSK) signals. Furthermore, compared to CMA and LKF, APA has the best tracking performance, and the tracking speed can be reached to 34-Mrad/s for PDM 16 quadrature amplitude modulation (PDM-16QAM) signal.

On the importance of feedback for categorization: Revisiting category learning experiments using an adaptive filter model.

Associative accounts of category learning have been, for the most part, abandoned in favor of cognitive explanations (e.g., similarity, explicit rules). In the current work, we implement an Adaptive Linear Filter (ALF) closely related to the Rescorla and Wagner learning rule, and use it to tackle three learning tasks that pose challenges to an associative view of category learning. Across three computational simulations, we show that the ALF is in fact able to make the predictions that seemed problematic. Notably, in our simulations we use exactly the same model and specifications, attesting to the generality of our account. We discuss the consequences of our findings for the category learning literature. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Компенсация искажений сигналов при распространении по трансионосферным радиолиниям с использованием глобальной модели земной ионосферы

A description is given of distortions of complex envelopes of digital signals during their propagation along transionospheric channels, the effect of which is equivalent to linear filtering. It is shown that signal distortions due to the dispersion properties of the earth's ionosphere cause the occurrence of interference noise which reduces the reliability of information transmission. It is noted that the effect of digital signal processing methods at reception, which reduce the distorting effect of interference is to form a linear filter with an inverse transmission coefficient relative to the transionospheric channels. A method for forming the inverse filter using the global model of the earth's ionosphere Klobuchar, developed and intensively used in the GPS satellite navigation system to improve the accuracy of navigation measurements is considered. A detailed description of this method is given, which is based on estimating the total electron content of a transionospheric channels using the considered Klobuchar model. Limitations in the application of the method under consideration are determined.

On the Genuine Relevance of the Data-Driven Signal Decomposition-Based Multiscale Permutation Entropy.

Ordinal pattern-based approaches have great potential to capture intrinsic structures of dynamical systems, and therefore, they continue to be developed in various research fields. Among these, the permutation entropy (PE), defined as the Shannon entropy of ordinal probabilities, is an attractive time series complexity measure. Several multiscale variants (MPE) have been proposed in order to bring out hidden structures at different time scales. Multiscaling is achieved by combining linear or nonlinear preprocessing with PE calculation. However, the impact of such a preprocessing on the PE values is not fully characterized. In a previous study, we have theoretically decoupled the contribution of specific signal models to the PE values from that induced by the inner correlations of linear preprocessing filters. A variety of linear filters such as the autoregressive moving average (ARMA), Butterworth, and Chebyshev were tested. The current work is an extension to nonlinear preprocessing and especially to data-driven signal decomposition-based MPE. The empirical mode decomposition, variational mode decomposition, singular spectrum analysis-based decomposition and empirical wavelet transform are considered. We identify possible pitfalls in the interpretation of PE values induced by these nonlinear preprocessing, and hence, we contribute to improving the PE interpretation. The simulated dataset of representative processes such as white Gaussian noise, fractional Gaussian processes, ARMA models and synthetic sEMG signals as well as real-life sEMG signals are tested.

Finite-time dynamic surface control using a novel nonlinear filter for nonlinear systems with input saturation and output constraint

This paper proposes a finite-time dynamic surface control (FTDSC) scheme using a novel nonlinear filter for nonlinear systems with input saturation and output constraint. The FTDSC scheme featured by nonlinear filter is presented to overcome the drawback of the traditional DSC scheme using first-order linear filter. The barrier Lyapunov function (BLF) is used to handling output constraint and the disadvantage of conventional input saturation problem is solved through introducing a nonlinear smooth function. In order to deal with the impact of external disturbance, the nonlinear disturbance observer (NDO) is introduced to estimate the disturbance. It is proved that All signals are semi-globally uniformly ultimately bounded (SGUUB) in the closed loop system. Moreover, the tracking error can convergences to a neighborhood of zero through the proper designed parameters. Comparison studies are conducted to verify that the proposed FTDSC scheme comparing with the traditional DSC scheme has the more accurate tracking capability.

ε-arithmetics for real vectors and linear processing of real vector-valued signals

In this paper, we introduce a new concept, namely ε-arithmetics, for real vectors of any fixed dimension. The basic idea is to use vectors of rational values (called rational vectors) to approximate vectors of real values of the same dimension within ε range. For rational vectors of a fixed dimension m, they can form a field that is an mth order extension Q(α) of the rational field Q where α has its minimal polynomial of degree m over Q. Then, the arithmetics, such as addition, subtraction, multiplication, and division, of real vectors can be defined by using that of their approximated rational vectors within ε range. We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences (signals) of finite length. With these newly defined concepts for real vectors, linear processing, such as linear filtering, ARMA modeling, and least squares fitting, can be implemented to real vector-valued signals with real vector-valued coefficients, which will broaden the existing linear processing to scalar-valued signals.

RNN-Based Demodulation Framework for Spectrum Narrowing in Ultra-Dense WDM Networks

To cope with the continuous traffic growth, spectral efficiency needs to be enhanced. Ultra-dense WDM systems, where narrower guard-bands are inserted between wavelength-division-multiplexed (WDM) signals than those used in conventional dense WDM (DWDM) systems, are expected to offer higher spectral efficiency. However, such systems are hindered by the spectrum narrowing induced by wavelength selective switches (WSSs) at nodes. As a result, intersymbol interference (ISI) can be excessive. Linear digital filters widely used in typical digital coherent receivers can equalize the ISI. However, ISI equalization yields noise enhancement due to the interaction between ISI and amplifier noise. Sequence estimation can alleviate the impact of this interaction; however, to introduce sequence estimation into real systems, an ISI-imposing filter is needed because the adaptive filter used for polarization recovery automatically equalizes the ISI. Although the optimum ISI-imposing filter can be created with the proper spectrum model, its characteristics change frequently in real optical path networks. Therefore, we need to develop a demodulation framework that does not necessitate any spectrum models. In this letter, we propose a novel demodulation framework that uses a recurrent neural network (RNN) to simultaneously realize the ISI-imposing filter and sequence estimator. Extensive computer simulations show that our proposal increases the transmission distance in ultra-dense WDM networks.

Specular Reflection Suppression through the Adjustment of Linear Polarization for Tumor Diagnosis Using Fluorescein Sodium.

In tumor surgery, the edges of the tumor can be visually observed using a fluorescent contrast agent and a fluorescent imaging device. By distinguishing it from normal tissues and blood vessels, it is possible to objectively judge the extent of resection while visually observing it during surgery, and it guarantees safe tumor resection based on more information. However, the main problem of such an imaging device is the specular reflection phenomenon. If specular reflection overlaps with important lesion locations, they are a major factor leading to diagnostic errors. Here, we propose a method to reduce specular reflection that occurs during tumor diagnosis using a linear polarization filter and fluorescent contrast agent. To confirm the effect of removing specular reflection, a self-made fluorescein sodium vial phantom was used, and the reliability of the results was increased using a large animal (pig) test. As a result of the experiment, it was possible to obtain an image in which specular reflection was removed by controlling the rotation angle of the filter by 90° and 270°, and the same results were confirmed in the phantom experiment and the animal experiment.

Prescribed Performance Fuzzy Adaptive Output Feedback Control for Nonlinear MIMO Systems in a Finite Time

This article studies the fuzzy adaptive output feedback control design problem for nonstrict feedback multi-input–multi-output nonlinear systems with full-states prescribed performance in finite time. Fuzzy logic systems are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining the adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to the traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full-states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on the Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semiglobal practical finite-time stability. Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided.

Blind Equalization and Channel Estimation in Coherent Optical Communications Using Variational Autoencoders

We investigate the potential of adaptive blind equalizers based on variational inference for carrier recovery in optical communications. These equalizers are based on a low-complexity approximation of maximum likelihood channel estimation. We generalize the concept of variational autoencoder (VAE) equalizers to higher order modulation formats encompassing probabilistic constellation shaping (PCS), ubiquitous in optical communications, oversampling at the receiver, and dual-polarization transmission. Besides black-box equalizers based on convolutional neural networks, we propose a model-based equalizer based on a linear butterfly filter and train the filter coefficients using the variational inference paradigm. As a byproduct, the VAE also provides a reliable channel estimation. We analyze the VAE in terms of performance and flexibility over a classical additive white Gaussian noise (AWGN) channel with inter-symbol interference (ISI) and over a dispersive linear optical dual-polarization channel. We show that it can extend the application range of blind adaptive equalizers by outperforming the state-of-the-art constant-modulus algorithm (CMA) for PCS for both fixed but also time-varying channels. The evaluation is accompanied with a hyperparameter analysis.

Adaptive Fuzzy Fixed-Time Tracking Control for Switched High-Order Multi-Agent Systems With Input Delay

This paper investigates the adaptive fuzzy fixed-time-based distributed consensus tracking control for non-strict feedback nonlinear switched high-order multi-agent systems (MASs) with completely unknown function, input delay, switched behavior dynamics (possibly asynchronous) and high powers (possibly different). In this work, the “explosive of complexity” issue is overcome by designing an improved fixed-time-based nonlinear filter. Unlike traditional linear filters, this paper skillfully introduces auxiliary terms (tanh function and cubic function) into each filter, which can completely compensate the effects resulted by filter errors and ensure the closed-loop system fixed-time convergence. Meanwhile, input delay is deal with a robust compensation signal constructed via a finite integral of the past control values. Besides, this paper adopts separable function technique to avoid the control gain of each virtual controller appearing in the next virtual controller, thus reducing the complexity of control actions. In the backstepping framework, a distributed fixed-time-based control scheme was presented, which can ensure that all the closed-loop signals are bounded within a fixed-time. Numerical simulation and practical example further verify the effectiveness of the developed control scheme.

Dipolarization-induced energetic electron precipitation during continuously active periods and isolated substorms

Recently we proposed a spatio-temporal model of auroral absorption for isolated substorms based on linear prediction filter technique, which describes the precipitation effects as a sum of properly weighted and time-delayed contributions of short dipolarizations/injections inferred from magnetic MPB index. Here we apply a similar approach to a more general and practically important type of continuous activity including substorms clusters, which is accompanied by intense energetic electron precipitation lasting for many hours and may affect ozone concentration and climate. Unexpectedly, in spite of very different geophysical background, the derived precipitation response to unit-scale injection appeared almost identical to that obtained for isolated substorms. Significant part of absorption variance during active non-storm periods turns out to be the result of superposition of previous injections with short memory less than 4 h. Our results indicate that, while the injection efficiency is roughly the same, large difference in precipitated fluxes and ionospheric response between two different types of activity is mostly provided by a more frequent appearance and increased intensities of dipolarizations/injections during active periods. In both event types dipolarizations are the decisive factor which determines energetic electron precipitation.

Removing systematics-induced 21-cm foreground residuals by cross-correlating filtered data

Observations of the redshifted 21-cm signal emitted by neutral hydrogen represent a promising probe of large-scale structure in the universe. However, cosmological 21-cm signal is challenging to observe due to astrophysical foregrounds which are several orders of magnitude brighter. Traditional linear foreground removal methods can optimally remove foregrounds for a known telescope response but are sensitive to telescope systematic errors such as antenna gain and delay errors, leaving foreground contamination in the recovered signal. Non-linear methods such as principal component analysis, on the other hand, have been used successfully for foreground removal, but they lead to signal loss that is difficult to characterize and requires careful analysis. In this paper, we present a systematics-robust foreground removal technique which combines both linear and non-linear methods. We first obtain signal and foreground estimates using a linear filter. Under the assumption that the signal estimate is contaminated by foreground residuals induced by parameterizable systematic effects, we infer the systematics-induced contamination by cross-correlating the initial signal and foreground estimates. Correcting for the inferred error, we are able to subtract foreground contamination from the linearly filtered signal up to the first order in the amplitude of the telescope systematics. In simulations of an interferometric 21-cm survey, our algorithm removes foreground leakage induced by complex gain errors by one to two orders of magnitude in the power spectrum. Our technique thus eases the requirements on telescope characterization for modern and next-generation 21-cm cosmology experiments.

Temporal Dynamics of Neural Responses in Human Visual Cortex.

Neural responses to visual stimuli exhibit complex temporal dynamics, including subadditive temporal summation, response reduction with repeated or sustained stimuli (adaptation), and slower dynamics at low contrast. These phenomena are often studied independently. Here, we demonstrate these phenomena within the same experiment and model the underlying neural computations with a single computational model. We extracted time-varying responses from electrocorticographic recordings from patients presented with stimuli that varied in duration, interstimulus interval (ISI) and contrast. Aggregating data across patients from both sexes yielded 98 electrodes with robust visual responses, covering both earlier (V1-V3) and higher-order (V3a/b, LO, TO, IPS) retinotopic maps. In all regions, the temporal dynamics of neural responses exhibit several nonlinear features. Peak response amplitude saturates with high contrast and longer stimulus durations, the response to a second stimulus is suppressed for short ISIs and recovers for longer ISIs, and response latency decreases with increasing contrast. These features are accurately captured by a computational model composed of a small set of canonical neuronal operations, that is, linear filtering, rectification, exponentiation, and a delayed divisive normalization. We find that an increased normalization term captures both contrast- and adaptation-related response reductions, suggesting potentially shared underlying mechanisms. We additionally demonstrate both changes and invariance in temporal response dynamics between earlier and higher-order visual areas. Together, our results reveal the presence of a wide range of temporal and contrast-dependent neuronal dynamics in the human visual cortex and demonstrate that a simple model captures these dynamics at millisecond resolution.SIGNIFICANCE STATEMENT Sensory inputs and neural responses change continuously over time. It is especially challenging to understand a system that has both dynamic inputs and outputs. Here, we use a computational modeling approach that specifies computations to convert a time-varying input stimulus to a neural response time course, and we use this to predict neural activity measured in the human visual cortex. We show that this computational model predicts a wide variety of complex neural response shapes, which we induced experimentally by manipulating the duration, repetition, and contrast of visual stimuli. By comparing data and model predictions, we uncover systematic properties of temporal dynamics of neural signals, allowing us to better understand how the brain processes dynamic sensory information.

Universal Graph Filter Design Based on Butterworth, Chebyshev, and Elliptic Functions

Graph filters are crucial tools in processing the spectrum of graph signals. In this paper, we propose to design universal IIR graph filters with low computational complexity by using three kinds of functions, which are Butterworth, Chebyshev, and elliptic functions, respectively. Specifically, inspired by the classical analog filter design method, we first derive the zeros and poles of graph frequency responses. With these zeros and poles, we construct the conjugate graph filters to design the Butterworth high-pass graph filter, Chebyshev high-pass graph filter, and elliptic high-pass graph filter, respectively. On this basis, we further propose to construct a desired graph filter of low pass, band pass, and band stop by mapping the parameters of the desired graph filter to those of the equivalent high-pass graph filter. Furthermore, we propose to set the graph filter order given the maximum passband attenuation and the minimum stopband attenuation. Our numerical results show that the proposed graph filter design methods realize the desired frequency response more accurately than the autoregressive moving average graph filter design method, the linear least-squares fitting-based graph filter design method, and the Chebyshev FIR polynomial graph filter design method.

Eliminating white noise in spectra: A generalized maximum-entropy approach

In linear filtering, high-frequency (white) noise is reduced by apodization, which is the attenuation or elimination of high-order Fourier coefficients followed by an inverse transformation. Unfortunately, apodization requires compromises to be made among noise leakage, information loss, and Gibbs oscillations. These shortcomings are avoided with the corrected maximum-entropy (CME) procedure, but this procedure applies only to Lorentzian or approximately Lorentzian features. We develop a generalized maximum-entropy method based on partial Hilbert transforms that allows CME to be applied to any spectrum, thereby eliminating white-noise completely with no deleterious side effects. As Hilbert transforms are exact Kramers–Kronig replicas of the original endpoint-discontinuity-corrected segment, new spectral processing opportunities are also realized.

Application and Optimization of Luenberger Observer Phase-Locked Loop and Inductance-Free Vector Control Method for Aviation Three-Phase Converter in Wearable Equipment.

This work aims to strengthen the comprehensive performance of the Luenberger observer in the application of aviation three-phase converter and in physical exercise wearable devices to effectively detect human physiological signals. Firstly, the use status and characteristics of three-phase converters are discussed. Then, the Luenberger observer and its optimization process are described. Finally, the Luenberger observer is optimized through phase-locked loop technology and the vector control method. The experimental results indicate that the PLL of the steady-state linear Kalman filter is applicable to the multielectric aircraft converter for the aviation variable frequency power supply. The phase-locked loop of the steady-state linear Kalman filter is complicated, and the output angular frequency is inconsistent with the angular frequency of the actual voltage of the aircraft variable-frequency power supply. Consequently, it does not have the function of frequency locking. On the contrary, the Luenberger observer phase-locked loop designed here is suitable for the multielectric aircraft converter for the aircraft variable-frequency power supply. In addition, it is simpler than the steady-state linear Kalman filter phase-locked loop and realizes the frequency-locking function. In addition, the vector control method significantly improves the control performance of the Luenberger observer. The control error of the original observer is about 0.24°, and the control error of the optimized observer is about 0.18°. This work provides technical support for the performance optimization of the Luenberger observer and contributes to the performance improvement of the aviation three-phase converter.

A novel Large Eddy Simulation model for the Quasi-Geostrophic equations in a Finite Volume setting

We present a Large Eddy Simulation (LES) approach based on a nonlinear differential low-pass filter for the simulation of two-dimensional barotropic flows with under-refined meshes. For the implementation of such model, we choose a segregated three-step algorithm combined with a computationally efficient Finite Volume method. We assess the performance of our approach with the classical double-gyre wind forcing benchmark. The numerical experiments we present demonstrate that our nonlinear filter is an improvement over a linear filter since it is able to recover the four-gyre pattern of the time-averaged stream function even with extremely coarse meshes. In addition, our LES approach provides an average kinetic energy that compares well with the one computed with a Direct Numerical Simulation.