Constituent Filters Research Articles

Design of fractional-order transitional filters of the Butterworth-Sync-Tuned, Butterworth-Chebyshev, and Chebyshev-Sync-Tuned types: optimization, simulation, and experimental verification

This paper presents the optimal and generalized design of three different fractional-order (FO) transitional filters for the first time in the literature. The transitional filters considered are of the FO Butterworth-sync-tuned, the FO Butterworth-Chebyshev, and the FO Chebyshev-sync-tuned types. A metaheuristic swarm intelligence optimizer, namely the Crow Search Algorithm (CSA), helps to achieve the optimal FO filter model that minimizes the magnitude error with the theoretical function. The accuracy of the proposed approximants is examined for 19 different combinations of orders of the constituent filters for each of the three types of FO transitional filters. Comparisons with the modified stability boundary locus-based second-, third-, and fourth-order filter approximants demonstrate the compactness and superior accuracy of the proposed models. The average performance regarding the approximation accuracy, computational time, and convergence of CSA for solving the proposed filter design problems is investigated. Circuit simulations conducted on the OrCAD PSPICE platform for the proposed filter using the current feedback operational amplifier as an active element highlight good matching between the proposed model and theoretical filter function. Experimental validation is also carried out to justify the practical feasibility of the proposed filter with printed circuit board fabricated FO capacitor emulators.

All-electrical valley filtering in graphene systems (II): Numerical study of electron transport in valley valves

This work performs a numerical study of electron transport through the fundamental logic gate in valleytronics—a valley valve consisting of two or increasing number of valley filters. Various typical effects on the transport are investigated, such as those due to interface scattering, long- and short-range impurity scattering, edge roughness, strain, inter-filter spacing, or increasing number of valley filters. For illustration, we consider the class of specific valves built from graphene quantum wire valley filters in single layer or bilayer graphene, with the filters subject to separate control of in-plane, transverse electric fields. The nearest-neighbor tight-binding model of graphene is used to formulate the corresponding transport problem, and the algorithm of the recursive Green's function method is applied to solve for the corresponding transmission coefficient. In the case of two-filter valves, the result explicitly demonstrates the existence of a pronounced on-off contrast in electron transmission between the two configurations of valves, namely, one with identical and the other with opposite valley polarities in the two constituent filters. The contrast is shown to be enhanced when increasing the number of filters in valves. Signatures of Fano–Fabry–Pérot type resonances in association with interface scattering and inter-filter spacing are illustrated. Electron backscattering due to impurities is found to be sizably suppressed, with the valve performance showing considerable robustness against edge roughness scattering. On the other hand, the presence of a uniaxial strain modifies the electron transmission and results in an interesting quasi-periodic modulation of transmission as we vary the strain strength.

Improving query performance on dynamic graphs

Querying large models efficiently often imposes high demands on system resources such as memory, processing time, disk access or network latency. The situation becomes more complicated when data are highly interconnected, e.g. in the form of graph structures, and when data sources are heterogeneous, partly coming from dynamic systems and partly stored in databases. These situations are now common in many existing social networking applications and geo-location systems, which require specialized and efficient query algorithms in order to make informed decisions on time. In this paper, we propose an algorithm to improve the memory consumption and time performance of this type of queries by reducing the amount of elements to be processed, focusing only on the information that is relevant to the query but without compromising the accuracy of its results. To this end, the reduced subset of data is selected depending on the type of query and its constituent filters. Three case studies are used to evaluate the performance of our proposal, obtaining significant speedups in all cases.

Direct estimation of NIR reflection spectra utilizing a snapshot-type spectrometer with photonic crystal multi-spectral filter arrays.

We fabricated 16-, 25-, 36-, and 64-channel distributed passband-type multi-spectral filter arrays by utilizing a multilayer-type photonic crystal and integrated them onto a CCD to form a snapshot-type spectroscopic sensor. Reflection spectra from target objects (fruits) under broadband light illumination were estimated directly using the Wiener estimation method. A root mean square error of the reflectivity on the order of 2∼5% was obtained under optical shot noise with 6×6 pixel binning. A number of constituent filters of 36 was sufficient for this type of fruit spectral measurement. We also visualized reflection images at specified wavelengths by applying the estimation method to a multiple filter region on the sensor.

An adaptive convex combination of APA and ZA-APA for identifying systems having variable sparsity and correlated input

In this paper, we present an efficient algorithm for identifying and tracking the impulse response of a sparse system that exhibits time varying sparseness and is driven by correlated input. The proposed method convexly combines the outputs of two filters, namely, the sparsity unaware affine projection algorithm (APA), and the sparsity aware zero attracting affine projection algorithm (ZA-APA), each trying to identify the same system using the same input. The combining parameter is adapted by following a steepest descent of the error variance at the convex combination output. A detailed performance analysis of the proposed combination is carried out, which reveals that while for highly non-sparse and highly sparse systems, the proposed combination converges respectively to the APA and ZA-APA (i.e., better of the two filters under the given levels of sparsity), for certain sparsity ranges, it leads to a combination filter that performs better than both the constituent filters. The claims made are validated by exhaustive simulation studies using white, colored as well as speech inputs.

A Convex Combination of NLMS and ZA-NLMS for Identifying Systems With Variable Sparsity

This brief aims to identify and track a sparse system with time varying sparseness by a convex combination of two adaptive filters, one based on the sparsity unaware normalized least mean square (NLMS) algorithm and the other based on the sparsity aware zero-attracting NLMS (ZA-NLMS) algorithm. An analysis of the proposed combination is carried out, which reveals that while the proposed combination converges to the ZA-NLMS or the NLMS-based filter for systems that are highly sparse or highly non-sparse, respectively (i.e., better of the two under the given sparsity condition), it may, however, lead to a filter that performs better than both the constituent filters in the case of systems that lie between moderately sparse to moderately non-sparse. The same is confirmed via detailed simulation studies under different sparsity conditions.

Computationally highly efficient mixture of adaptive filters

We introduce a new combination approach for the mixture of adaptive filters based on the set-membership filtering (SMF) framework. We perform SMF to combine the outputs of several parallel running adaptive algorithms and propose unconstrained, affinely constrained and convexly constrained combination weight configurations. Here, we achieve better trade-off in terms of the transient and steady-state convergence performance while providing significant computational reduction. Hence, through the introduced approaches, we can greatly enhance the convergence performance of the constituent filters with a slight increase in the computational load. In this sense, our approaches are suitable for big data applications where the data should be processed in streams with highly efficient algorithms. In the numerical examples, we demonstrate the superior performance of the proposed approaches over the state of the art using the well-known datasets in the machine learning literature.

Performance Analysis and Optimal Design of Multichannel Equalizer for Underwater Acoustic Communications

Adaptive equalization is a widely used method of mitigating the effects of multipath propagation and Doppler spreading in underwater acoustic communication channels. While the structure of a multichannel equalizer and least-squares-based adaptation algorithm are extensively used in practice, little is known in how to choose the number of sensors, separation between them, and lengths of the constituent filters such that the equalization performance is optimized. This paper studies the problem of optimal multichannel equalizer design in the context of time-varying underwater acoustic communication channels. In the first part, the paper presents a theoretical characterization of the equalization performance when the number of symbols that can be received in the time period over which the channel can be considered time invariant is limited. This result is then used to develop an understanding that the optimal number of equalizer coefficients is a tradeoff between the minimum mean squared error (MMSE) requirement for longer constituent filters and the insight that the limit on the number of stationary observations also limits the number of filter coefficients that can be effectively adapted. In the second part, the paper develops a theoretical model for wideband arrivals impinging upon an array of sensors of the multichannel equalizer. This model is used to develop an understanding that the optimal sensor separation is a tradeoff between the requirement for long aperture which improves resolution, and the fact that the grating lobes, caused by spatial undersampling, limit the equalizer’s ability to estimate the transmitted signal from the received signal.

The Krylov-proportionate normalized least mean fourth approach: Formulation and performance analysis

We propose novel adaptive filtering algorithms based on the mean-fourth error objective while providing further improvements on the convergence performance through proportionate update. We exploit the sparsity of the system in the mean-fourth error framework through the proportionate normalized least mean fourth (PNLMF) algorithm. In order to broaden the applicability of the PNLMF algorithm to dispersive (non-sparse) systems, we introduce the Krylov-proportionate normalized least mean fourth (KPNLMF) algorithm using the Krylov subspace projection technique. We propose the Krylov-proportionate normalized least mean mixed norm (KPNLMMN) algorithm combining the mean-square and mean-fourth error objectives in order to enhance the performance of the constituent filters. Additionally, we propose the stable-PNLMF and stable-KPNLMF algorithms overcoming the stability issues induced due to the usage of the mean fourth error framework. Finally, we provide a complete performance analysis, i.e., the transient and the steady-state analyses, for the proportionate update based algorithms, e.g., the PNLMF, the KPNLMF algorithms and their variants; and analyze their tracking performance in a non-stationary environment. Through the numerical examples, we demonstrate the match of the theoretical and ensemble averaged results and show the superior performance of the introduced algorithms in different scenarios.

Sparse Adaptive Filtering by an Adaptive Convex Combination of the LMS and the ZA-LMS Algorithms

In practice, one often encounters systems that have a sparse impulse response, with the degree of sparseness varying over time. This paper presents a new approach to identify such systems which adapts dynamically to the sparseness level of the system and thus works well both in sparse and non-sparse environments. The proposed scheme uses an adaptive convex combination of the LMS algorithm and the recently proposed, sparsity-aware zero-attractor LMS (ZA-LMS) algorithm. It is shown that while for non-sparse systems, the proposed combined filter always converges to the LMS algorithm (which is better of the two filters for non-sparse case in terms of lesser steady state excess mean square error (EMSE)), for semi-sparse systems, on the other hand, it actually converges to a solution that produces lesser steady state EMSE than produced by either of the component filters. For highly sparse systems, depending on the value of a proportionality constant in the ZA-LMS algorithm, the proposed combined filter may either converge to the ZA-LMS based filter or may produce a solution which, like the semi-sparse case, outperforms both the constituent filters. A simplified update formula for the mixing parameter of the adaptive convex combination is also presented. The proposed algorithm requires much less complexity than the existing algorithms and its claimed robustness against variable sparsity is well supported by simulation results.

Peformance Analysis of Mixture Approaches and Tracking Performance of Adaptive Filter using Adaptive Neural Network

paper mainly concentrates on different mixture structures which include affine and convex combinations of several parallel running adaptive filters. The mixture structures are investigated using their final MSE values and the tracking of the nonlinear system is done using an ANN model that updates the filter weights using nonlinear learning strategies(it uses stochastic gradient descent to update the filter weights based on MSE's of mixture structures).the mixture structures greatly improve the convergence and performance of the of the constituent filters compared to traditional adaptive methods. The mixture structures employed in this paper can be applied to the constituent filters that employ different adaptation algorithms. We describe an adaptive neural network model that updates the weights of the filter using nonlinear methods.

Adaptive mixture methods based on Bregman divergences

We investigate adaptive mixture methods that linearly combine outputs of $m$ constituent filters running in parallel to model a desired signal. We use "Bregman divergences" and obtain certain multiplicative updates to train the linear combination weights under an affine constraint or without any constraints. We use unnormalized relative entropy and relative entropy to define two different Bregman divergences that produce an unnormalized exponentiated gradient update and a normalized exponentiated gradient update on the mixture weights, respectively. We then carry out the mean and the mean-square transient analysis of these adaptive algorithms when they are used to combine outputs of $m$ constituent filters. We illustrate the accuracy of our results and demonstrate the effectiveness of these updates for sparse mixture systems.

Active control of nonlinear noise processes using cascaded adaptive nonlinear filter

A novel nonlinear adaptive filter based on a cascade combination of a functional link artificial neural network (FLANN) and a Legendre polynomial has been proposed in this paper for nonlinear active noise control (ANC). The performance of the new controller has been compared with that obtained by a FLANN based ANC system trained using a filtered-s least mean square (FsLMS) algorithm as well as with a Legendre neural network (LeNN) based ANC system trained using a filtered-l LMS (FlLMS) algorithm. The training of the cascaded controller has been achieved using a filtered-sl LMS (FslLMS) algorithm, which simultaneously adapts the weights of both the component adaptive controllers. The new controller has been shown to achieve improved noise mitigation capability in comparison to its constituent filters.

Steady State and Transient MSE Analysis of Convexly Constrained Mixture Methods

We investigate convexly constrained mixture methods to adaptively combine outputs of two adaptive filters running in parallel to model a desired unknown system. We compare several algorithms with respect to their mean-square error in the steady state, when the underlying unknown system is nonstationary with a random walk model. We demonstrate that these algorithms are universal such that they achieve the performance of the best constituent filter in the steady state if certain algorithmic parameters are chosen properly. We also demonstrate that certain mixtures converge to the optimal convex combination filter such that their steady-state performances can be better than the best constituent filter. We also perform the transient analysis of these updates in the mean and mean-square error sense. Furthermore, we show that the investigated convexly constrained algorithms update certain auxiliary variables through sigmoid nonlinearity, hence, in this sense, related.

Transient Analysis of Adaptive Affine Combinations

In this correspondence, we provide a transient analysis of an affinely constrained mixture method that adaptively combines the outputs of adaptive filters running in parallel on the same task. The affinely constrained mixture is adapted using a stochastic gradient update to minimize the square of the prediction error. Although we specifically carry out the transient analysis for a combination of two equal length adaptive filters trying to learn a linear model working on real valued data, we also provide the final equations and the necessary extensions in order to generalize the transient analysis to mixtures combining more than two filters; using Newton based updates to train the mixture weights; working on complex valued data; or unconstrained mixtures. The derivations are generic such that the constituent filters can be trained using unbiased updates including the least-mean squares or recursive least squares updates. This correspondence concludes with numerical examples and final remarks.

Design of Multiplierless Decimation Filters Using an Extended Search of Cyclotomic Polynomials

This brief addresses the design of multiplierless decimation filters using an extended set of cyclotomic polynomials (CPs) as constituent filters. It extends the results presented in a companion paper by one of the coauthors to CPs with indexes in the set <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\{\hbox{1},\, \ldots,\, \hbox{200}\}$ </tex></formula> , and it presents the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$z$</tex></formula> -transfer functions of all CPs with indexes from 61 to 200. One of the key observations stemming from the results of this brief is that CPs with indexes in the set <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\{\hbox{105},\, \ldots,\, \hbox{200}\}$</tex></formula> still have very effective coefficients, i.e., integers belonging to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\{-\hbox{1}, \, \hbox{0}, +\hbox{1}\,\}$</tex></formula> , but <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$z$</tex></formula> -transfer functions have to be recursive. Regardless of the application to multirate filters considered in this brief, these polynomials can also be used for designing classical finite-impulse response filters. Moreover, this brief provides guidelines to simplify the design of constituent decimation filters in multistage architectures and to reduce computational complexity of the proposed filters. Finally, comparisons are given with respect to other techniques in the literature.

Steady-State MSE Performance Analysis of Mixture Approaches to Adaptive Filtering

In this paper, we consider mixture approaches that adaptively combine outputs of several parallel running adaptive algorithms. These parallel units can be considered as diversity branches that can be exploited to improve the overall performance. We study various mixture structures where the final output is constructed as the weighted linear combination of the outputs of several constituent filters. Although the mixture structure is linear, the combination weights can be updated in a highly nonlinear manner to minimize the final estimation error such as in Singer and Feder 1999; Arenas-Garcia, Figueiras-Vidal, and Sayed 2006; Lopes, Satorius, and Sayed 2006; Bershad, Bermudez, and Tourneret 2008; and Silva and Nascimento 2008. We distinguish mixture approaches that are convex combinations (where the linear mixture weights are constrained to be nonnegative and sum up to one) [Singer and Feder 1999; Arenas-Garcia, Figueiras-Vidal, and Sayed 2006], affine combinations (where the linear mixture weights are constrained to sum up to one) [Bershad, Bermudez, and Tourneret 2008] and, finally, unconstrained linear combinations of constituent filters [Kozat and Singer 2000]. We investigate mixture structures with respect to their final mean-square error (MSE) and tracking performance in the steady state for stationary and certain nonstationary data, respectively. We demonstrate that these mixture approaches can greatly improve over the performance of the constituent filters. Our analysis is also generic such that it can be applied to inhomogeneous mixtures of constituent adaptive branches with possibly different structures, adaptation methods or having different filter lengths.

Unbiased Model Combinations for Adaptive Filtering

In this paper, we consider model combination methods for adaptive filtering that perform unbiased estimation. In this widely studied framework, two adaptive filters are run in parallel, each producing unbiased estimates of an underlying linear model. The outputs of these two filters are combined using another adaptive algorithm to yield the final output of the system. Overall, we require that the final algorithm produce an unbiased estimate of the underlying model. We later specialize this framework where we combine one filter using the least-mean squares (LMS) update and the other filter using the least-mean fourth (LMF) update to decrease cross correlation in between the outputs and improve the overall performance. We study the steady-state performance of previously introduced methods as well as novel combination algorithms for stationary and nonstationary data. These algorithms use stochastic gradient updates instead of the variable transformations used in previous approaches. We explicitly provide steady-state analysis for both stationary and nonstationary environments. We also demonstrate close agreement with the introduced results and the simulations, and show for this specific combination, more than 2 dB gains in terms of excess mean square error with respect to the best constituent filter in the simulations.

Generalized polyphase structure-based Mth-band filter design and application to image interpolation

A generalized polyphase (GP) structure-based method for the design of linear-phase Mth-band FIR filters satisfying the time-domain interpolation condition is presented. Some new transform matrices that allow for the use of an arbitrary number of branches in the GP structure are developed. Closed-form frequency specifications for constituent filters of the GP realization are obtained, making an independent and fast design of the short-length constituent filters possible. The proposed GP-based method is then extended for the design of a class of interpolation filters with certain regularities. Some of the interpolation filters designed based on the proposed GP structure are also applied to image resizing. Simulation results show that our interpolation filter gives a superior resized image than the common cubic spline interpolation does.

New Perspectives and Improvements on the Symmetric Extension Filter Bank for Subband/Wavelet Image Compression

In subband/wavelet image coding, size-limited subband decompositions are ordinarily used to avoid increasing the number of samples that need to be coded. To reduce coding distortions that can occur at the borders, the symmetric extension filter bank is typically employed. This paper introduces some new perspectives and improvements to that decomposition. The symmetric extension filter bank is couched in the cyclic frequency domain, providing a framework that accommodates FIR and IIR filters in a natural way, all with perfect reconstruction. IIR filters with both rational and irrational transfer functions can be implemented and, in the context of symmetric extension, can accommodate IIRs that effectively have perfect stopband suppression. Enhancements to the filter bank at a tree-structured system level are also presented and include the application of spectral reversal correction and a transition band normalization approach to designing the constituent filters of the symmetric extension wavelet packet transform.