Journal articles: 'SQUARE FILTER'

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Nerger, Lars, Tijana Janjić, Jens Schröter, and Wolfgang Hiller. "A Unification of Ensemble Square Root Kalman Filters." Monthly Weather Review 140, no. 7 (July 1, 2012): 2335–45. http://dx.doi.org/10.1175/mwr-d-11-00102.1.

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Abstract In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular “evolutive” interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.

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Matei, Radu. "Design of Adjustable Square-Shaped 2D IIR Filters." ISRN Signal Processing 2013 (September 11, 2013): 1–10. http://dx.doi.org/10.1155/2013/796830.

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This paper proposes an analytical design method for two-dimensional square-shaped IIR filters. The designed 2D filters are adjustable since their bandwidth and orientation are specified by parameters appearing explicitly in the filter matrices. The design relies on a zero-phase low-pass 1D prototype filter. To this filter a frequency transformation is next applied, which yields a 2D filter with the desired square shape in the frequency plane. The proposed method combines the analytical approach with numerical approximations. Since the prototype transfer function is factorized into partial functions, the 2D filter also will be described by a factorized transfer function, which is an advantage in implementation.

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Tengger, Billy Arifa, and Ropiudin Ropiudin. "Pemanfaatan Metode Kalman Filter Diskrit untuk Menduga Suhu Udara." Square : Journal of Mathematics and Mathematics Education 1, no. 2 (December 31, 2019): 127. http://dx.doi.org/10.21580/square.2019.1.2.4202.

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Suhu adalah variabel fisik yang perlu diketahui secara tepat untuk penggunaan tertentu. Suhu adalah derajat panas dan dingin suatu benda. Derajat panas dan dingin ini dipengaruhi oleh enthalpi (energi) yang dimilki suatu zat. Pendugaan suhu udara dapat memberikan manfaat untuk aktivitas pada beberapa bidang, seperti: pertanian, peternakan, perikanan, kesehatan, dan kegiatan-kegiatan lainnya. Metode Kalman Filter Diskrit merupakan salah satu metode matematika yang dapat digunakan untuk menduga data di masa yang akan datang. Kalman Filter Diskrit memiliki keunggulan mampu menduga suatu kondisi berdasarkan data terbatas. Data pengukuran terbaru menjadi suatu bagian terpenting dalam algoritma Kalman Filter, karena data tersebut akan mengkoreksi data hasil pendugaan, sehingga hasil pendugaan selalu mendekati kondisi sesungguhnya. Berdasarkan hasil kajian yang telah dilakukan menggunakan metode Kalman Filter Diskrit untuk menduga suhu udara diperoleh ketepatan pendugaan nilai suhu udara di atas 95%. Pedugaan dilakukan secara harian dan bulanan. Dengan demikian Kalman Filter Diskrit mampu dan handal untuk pendugaan suhu udara secara harian, bulanan, bahkan tahunan.

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Huang, Yulong, Yonggang Zhang, Ning Li, and Lin Zhao. "Improved square-root cubature information filter." Transactions of the Institute of Measurement and Control 39, no. 4 (July 22, 2016): 579–88. http://dx.doi.org/10.1177/0142331215608428.

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In this paper, a theoretical comparison between existing the sigma-point information filter (SPIF) framework and the unscented information filter (UIF) framework is presented. It is shown that the SPIF framework is identical to the sigma-point Kalman filter (SPKF). However, the UIF framework is not identical to the classical SPKF due to the neglect of one-step prediction errors of measurements in the calculation of state estimation error covariance matrix. Thus SPIF framework is more reasonable as compared with UIF framework. According to the theoretical comparison, an improved cubature information filter (CIF) is derived based on the superior SPIF framework. Square-root CIF (SRCIF) is also developed to improve the numerical accuracy and stability of the proposed CIF. The proposed SRCIF is applied to a target tracking problem with large sampling interval and high turn rate, and its performance is compared with the existing SRCIF. The results show that the proposed SRCIF is more reliable and stable as compared with the existing SRCIF. Note that it is impractical for information filters in large-scale applications due to the enormous computational complexity of large-scale matrix inversion, and advanced techniques need to be further considered.

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Yang, X., and T. DelSole. "The diffuse ensemble filter." Nonlinear Processes in Geophysics 16, no. 4 (July 16, 2009): 475–86. http://dx.doi.org/10.5194/npg-16-475-2009.

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Abstract. A new class of ensemble filters, called the Diffuse Ensemble Filter (DEnF), is proposed in this paper. The DEnF assumes that the forecast errors orthogonal to the first guess ensemble are uncorrelated with the latter ensemble and have infinite variance. The assumption of infinite variance corresponds to the limit of "complete lack of knowledge" and differs dramatically from the implicit assumption made in most other ensemble filters, which is that the forecast errors orthogonal to the first guess ensemble have vanishing errors. The DEnF is independent of the detailed covariances assumed in the space orthogonal to the ensemble space, and reduces to conventional ensemble square root filters when the number of ensembles exceeds the model dimension. The DEnF is well defined only in data rich regimes and involves the inversion of relatively large matrices, although this barrier might be circumvented by variational methods. Two algorithms for solving the DEnF, namely the Diffuse Ensemble Kalman Filter (DEnKF) and the Diffuse Ensemble Transform Kalman Filter (DETKF), are proposed and found to give comparable results. These filters generally converge to the traditional EnKF and ETKF, respectively, when the ensemble size exceeds the model dimension. Numerical experiments demonstrate that the DEnF eliminates filter collapse, which occurs in ensemble Kalman filters for small ensemble sizes. Also, the use of the DEnF to initialize a conventional square root filter dramatically accelerates the spin-up time for convergence. However, in a perfect model scenario, the DEnF produces larger errors than ensemble square root filters that have covariance localization and inflation. For imperfect forecast models, the DEnF produces smaller errors than the ensemble square root filter with inflation. These experiments suggest that the DEnF has some advantages relative to the ensemble square root filters in the regime of small ensemble size, imperfect model, and copious observations.

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Psiaki, Mark L. "The Square Root Information Increment Ensemble Filter." Monthly Weather Review 144, no. 12 (November 9, 2016): 4667–86. http://dx.doi.org/10.1175/mwr-d-15-0295.1.

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Abstract A new type of ensemble filter is developed, one that stores and updates its state information in an efficient square root information filter form. It addresses two shortcomings of conventional ensemble Kalman filters: the coarse characterization of random forecast model error effects and the overly optimistic approximation of the estimation error statistics. The new filter uses an assumed a priori covariance approximation that is full rank but sparse, possibly with a dense low-rank increment. This matrix can be used to develop a nominal square root information equation for the system state and uncertainty. The measurements are used to develop an additional low-rank square root information equation. New algorithms provide forecasts and analyses of these increments at a computational cost comparable to that of existing ensemble Kalman filters. Model error effects are implicit in the a priori covariance time history, thereby obviating one of the reasons for including an inflation operation. The use of an a priori full-rank covariance allows the analysis operations to improve the state estimate without the need for a localization adjustment. This new filter exhibited worse performance than a typical covariance square root ensemble Kalman filter when operating on the Lorenz-96 problem in a chaotic regime. It excelled on a version of the Lorenz-96 problem where nonlinearities in the forecast model were weak, where the state vector uncertainty lay predominantly in a small subspace, and where the observations were spatially sparse. Such a problem might be representative of ionospheric space weather data assimilation where forcing variability can dominate the state uncertainty and where remote sensing data coverage can be sparse.

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Altaf, M. U., T. Butler, T. Mayo, X. Luo, C. Dawson, A. W. Heemink, and I. Hoteit. "A Comparison of Ensemble Kalman Filters for Storm Surge Assimilation." Monthly Weather Review 142, no. 8 (August 1, 2014): 2899–914. http://dx.doi.org/10.1175/mwr-d-13-00266.1.

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Abstract This study evaluates and compares the performances of several variants of the popular ensemble Kalman filter for the assimilation of storm surge data with the advanced circulation (ADCIRC) model. Using meteorological data from Hurricane Ike to force the ADCIRC model on a domain including the Gulf of Mexico coastline, the authors implement and compare the standard stochastic ensemble Kalman filter (EnKF) and three deterministic square root EnKFs: the singular evolutive interpolated Kalman (SEIK) filter, the ensemble transform Kalman filter (ETKF), and the ensemble adjustment Kalman filter (EAKF). Covariance inflation and localization are implemented in all of these filters. The results from twin experiments suggest that the square root ensemble filters could lead to very comparable performances with appropriate tuning of inflation and localization, suggesting that practical implementation details are at least as important as the choice of the square root ensemble filter itself. These filters also perform reasonably well with a relatively small ensemble size, whereas the stochastic EnKF requires larger ensemble sizes to provide similar accuracy for forecasts of storm surge.

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Mu, Jing, Yuan Li Cai, and Jun Min Zhang. "Square Root Cubature Particle Filter." Advanced Materials Research 219-220 (March 2011): 727–31. http://dx.doi.org/10.4028/www.scientific.net/amr.219-220.727.

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The square root cubature particle filter (SRCPF) uses the square root cubature Kalman filter (SRCKF) for generating the proposal distribution. The SRCPF algorithm is easy to be implemented and has numerical stability. Moreover, the SRCKF based proposal distribution approximates the optimal importance distribution by incorporating the current measurement. Simulation results demonstrate that the SRCPF algorithm has the better performance for state estimation than the generic particle filter (GPF), extended particle filter (EPF) and unscented particle filter (UPF), and its calculation cost decreases largely.

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9

Tödter, Julian, and Bodo Ahrens. "A Second-Order Exact Ensemble Square Root Filter for Nonlinear Data Assimilation." Monthly Weather Review 143, no. 4 (March 31, 2015): 1347–67. http://dx.doi.org/10.1175/mwr-d-14-00108.1.

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Abstract The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational data assimilation schemes and are applied in a wide range of operational and research activities. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the analysis mean and covariance are biased, and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) only relies on Bayes’s theorem, which guarantees an exact asymptotic behavior, but because of the so-called curse of dimensionality it is exposed to weight collapse. Here, it is shown how to obtain a new analysis ensemble whose mean and covariance exactly match the Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The properties and performance of the proposed algorithm are further investigated via a set of experiments. They indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. Localization enhances the potential applicability of this PF-inspired scheme in larger-dimensional systems. The proposed algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF).

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Bastioli, Simone, Luca Marcaccioli, and Roberto Sorrentino. "Compact dual-mode rectangular waveguide filters using square ridge resonators." International Journal of Microwave and Wireless Technologies 1, no. 4 (June 22, 2009): 241–47. http://dx.doi.org/10.1017/s1759078709990286.

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A new class of compact rectangular waveguide filters is proposed in this paper. The key element is a square ridge resonator realized within a rectangular waveguide supporting the fundamental TE10 mode. The square ridge can support two modes resonating along orthogonal directions in the gap between the ridge and the opposite waveguide wall. This structure enables dual-mode degeneracy without the need of oversized cavities, thus allowing for considerable size reduction with respect to the conventional dual-mode implementations. Different filter structures employing one or more ridges within short waveguide sections are proposed as attractive solutions for pseudo-elliptic band-pass or dual-band filters. The experimental results of a manufactured fourth-order pseudo-elliptic pass-band filter validate the feasibility of the proposed class of filters.

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11

Chandra, Kumar Pakki Bharani, Da-Wei Gu, and Ian Postlethwaite. "Square Root Cubature Information Filter." IEEE Sensors Journal 13, no. 2 (February 2013): 750–58. http://dx.doi.org/10.1109/jsen.2012.2226441.

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Pratiwi, Nor Kumalasari Caecar, Rita Magdalena, Yunendah Nur Fuadah, Sofia Saidah, Syamsul Rizal, and Muhamad Rokhmat Isnaini. "Denoising Sinyal EEG dengan Algoritma Recursive Least Square dan Least Mean Square." TELKA - Telekomunikasi, Elektronika, Komputasi dan Kontrol 5, no. 2 (November 27, 2019): 122–29. http://dx.doi.org/10.15575/telka.v5n2.122-129.

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EEG mengukur fluktuasi tegangan yang dihasilkan dari arus ionik yang beredar sepanjang neuron otak. Dalam pengaturan eksperimental, sinyal EEG sering terkontaminasi dengan berbagai noise akibat gerakan otot dan jantung. Noise dengan magnitudo yang lebih tinggi dari sinyal aslinya akan merusak sinyal EEG dan bisa berakibat fatal dalam analisis diagnosa. Sehingga diperlukan sebuah sistem denoising yang mampu secara maksimal mengurangi noise, tanpa menghilangkan komponen informasi penting dari sinyal EEG. Salah satu algoritma yang dapat digunakan dalam mereduksi noise pada sinyal biomedis adalah RLS dan LMS. Keuntungan utama dari penggunaan adaptif filtering termasuk RLS dan LMS adalah dapat digunakan pada lingkungan non-stasioner. Tujuan penelitian adalah melakukan uji perbandingan performansi filtering RLS dan LMS dalam mereduksi noise pada sinyal EEG. Parameter performansi yang diukur adalah waktu komputasi, MSE, SNR, dan PSNR. Dari hasil pengujian, diperoleh bahwa adaptif filtering dengan RLS dan LMS mampu mereduksi noise pada sinyal EEG dengan baik. Filter LMS memiliki kelebihan pada waktu komputasinya yang singkat, rata-rata waktu komputasi filter LMS selama 0.7 detik, jauh berbeda dengan filter RLS yang membutuhkan waktu sampai dengan 113 detik. Tetapi kehandalan sistem dari sisi MSE, SNR dan PSNR untuk filter LMS masih berada dibawah RLS untuk intensitas noise yang rendah. Besarnya parameter SNR dan PSNR pada filter RLS cenderung lebih stabil pada intesitas noise 10 dB, 20 dB, dan 30 db. Hal berbeda terjadi pada denoising dengan menggunakan filter LMS, terjadi perubahan SNR yang signifikan dari 16.14 dB pada noise 10 dB, 21.09 dB untuk noise sebesar 20 dB, dan 25.81 dB untuk intensitas noise sebesar 30 dB.

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Shao, Teng. "Distributed filtering in sensor networks based on linear minimum mean square error criterion with limited sensing range." International Journal of Distributed Sensor Networks 18, no. 7 (July 2022): 155013292211108. http://dx.doi.org/10.1177/15501329221110810.

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One of the fundamental problems in sensor networks is to estimate and track the target states of interest that evolve in the sensing field. Distributed filtering is an effective tool to deal with state estimation in which each sensor only communicates information with its neighbors in sensor networks without the requirement of a fusion center. However, in the majority of the existing distributed filters, it is assumed that typically all sensors possess unlimited field of view to observe the target states. This is quite restrictive since practical sensors have limited sensing range. In this article, we consider distributed filtering based on linear minimum mean square error criterion in sensor networks with limited sensing range. To achieve the optimal filter and consensus, two types of strategies based on linear minimum mean square error criterion are proposed, that is, linear minimum mean square error filter based on measurement and linear minimum mean square error filter based on estimate, according to the difference of the neighbor sensor information received by the sensor. In linear minimum mean square error filter based on measurement, the sensor node collects measurement from its neighbors, whereas in linear minimum mean square error filter based on estimate, the sensor node collects estimate from its neighbors. The stability and computational complexity of linear minimum mean square error filter are analyzed. Numerical experimental results further verify the effectiveness of the proposed methods.

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El Hafidi, Mustapha, Latifa Mouhir, Mohamed Laaouan, Amal Kabbour, and Laila Saafadi. "Domestic wastewater treatment by vertical filter planted with Papyrus Cyperus: the plant adaptation in the new environment." E3S Web of Conferences 150 (2020): 02014. http://dx.doi.org/10.1051/e3sconf/202015002014.

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The wastewater from rural areas or small agglomerations usually discharged in an unsuitable manner requires an appropriate treatment. The constructed wetland has revealed a great potential due to the good performance, reasonable investment and easier management. The aim of this article is to present the results of the adaptation period (45 days) of a substitute plant, Papyrus Cyperus, in the new environment. Investigations were carried out on a concrete vertical filter of 12 m2 filled with gravel available on the local market. Monitoring was provided mainly through two squares of 1 m2 each. The results were compared with a control square planted in natural soil. The filter and the control square were planted with a density of 3 plants / m2 and were fed by necessary water needs. At the completion of the adaptation phase, the density increased by 26 stems at each Square of the filter. The stems exceeded 1 m in height (Square 1: 110 cm ± 0.9, Square 2: 123.5 cm ± 0.7 and control Square: 113 cm ± 0.9). The mean perimeter exceeded 5 cm at the filter (square 1: 5.6 cm ± 0.5 and square 2: 5.5 cm ± 0.1) and almost 4 cm in the control square (3.7 cm ± 0, 2). The shoots reached during the last half of the adaptation period 20 shoots in the Squares of the filter and 16 shoots in the control square. It should be noted that the young stems are adapted quickly than the older ones. Papyrus Cyperus plants have completed this phase with good health (absence of disease symptoms) and organ development similar to control plants.

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Rahman, Aviv Yuniar, Mamba’us Sa’adah, and Istiadi. "Noise Reduction in RTL-SDR using Least Mean Square and Recursive Least Square." Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) 4, no. 2 (April 19, 2020): 286–95. http://dx.doi.org/10.29207/resti.v4i2.1667.

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Noise reduction is an important process in a communication system, one of which is radio communication. In the process of broadcasting radio Frequency Modulation (FM) often encountered noise so that listeners find it difficult to understand the information provided. In the past, noise reduction used traditional filters that were only able to filter certain frequencies. However, for future technologies an adaptive filter is needed that can dynamically reduce noise effectively. Register Level-Software Defined Radio (RTL-SDR) can capture signals with a very wide frequency range but has a less clear sound quality. So it needs to be done noise reduction. In this study, two methods are used, namely Least Mean Square (LMS) and Recursive Least Square (RLS). The data used five radio stations in Malang. The results showed that the LMS algorithm is stable but has a slow convergence speed, whereas the RLS algorithm has poor stability but has a high convergence speed. From the test, it can be concluded that the performance of RLS is better than LMS for noise reduction in RTL-SDR. The best performance is the reduction of White Noise using RLS on the Oryza radio station with an Normalized Weight Differences (NWD) value of -13.93 dB.

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Wu, Yunfeng, and Rangaraj M. Rangayyan. "An Unbiased Linear Adaptive Filter with Normalized Coefficients for the Removal of Noise in Electrocardiographic Signals." International Journal of Cognitive Informatics and Natural Intelligence 3, no. 4 (October 2009): 73–90. http://dx.doi.org/10.4018/jcini.2009062305.

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The authors propose an unbiased linear adaptive filter (ULAF) to eliminate high-frequency random noise in electrocardiographic (ECG) signals. The ULAF does not contain a bias in its summation unit, and the filter coefficients are normalized. During the adaptation process, the normalized coefficients are updated with the steepest-descent algorithm in order to achieve efficient filtering of noisy ECG signals. The authors tested the ULAF with ECG signals recorded from 16 subjects, and compared the performance of the ULAF with that of the least-mean-square (LMS) and recursive-least-squares (RLS) adaptive filters. The filtering performance was quantified in terms of the root-mean-squared error (RMSE), normalized correlation coefficient (NCC), and filtered noise entropy (FNE). A template derived from each ECG signal was used as the reference to compute the measures of filtering performance. The results indicated that the ULAF was able to provided noise-free ECG signals with an average RMSE of 0.0287, which was lower than the second best RMSE (0.0365) obtained with the LMS filter. With respect to waveform fidelity, the proposed ULAF provided the highest average NCC (0.9964) among the three filters studied. In addition, the ULAF effectively removed more noise measured by FNE versus the LMS and RLS filters in most of the ECG signals tested.

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Ali, Randall, Hannes Rosseel, and Toon van Waterschoot. "Design and implementation of a least-mean-square adaptive notch filter." Journal of the Acoustical Society of America 153, no. 3_supplement (March 1, 2023): A215. http://dx.doi.org/10.1121/10.0018697.

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The task of removing sinusoidal components from observed signals can be accomplished by using a notch filter with a specific attenuation at a particular frequency. In some applications, however, such as acoustic feedback control, the frequency at which attenuation is required is unknown and possibly time-varying, and hence an adaptive notch filter is a more appropriate solution. Transitioning from a fixed notch filter to an adaptive one is by no means trivial and involves the understanding of a range of digital signal processing (DSP) topics from pole-zero placement techniques for designing infinite impulse response filters to optimal and adaptive filtering algorithms. In the signal processing algorithms and implementation graduate course taught at KU Leuven (Belgium), we study the design of an adaptive notch filter, which is based on a constrained biquadratic IIR representation, andwhose parameters are updated using a least-mean-square algorithm. Students also have to implement the algorithm on a 16-bit DSP TMS320C5515. In this presentation, we will discuss the design and implementation challenges of this adaptive notch filter and how it serves as an illustrative example/homework problem where several aspects of DSP are interwoven.

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Li, Jing, and Jiaxu Zhang. "Vehicle Sideslip Angle Estimation Based on Hybrid Kalman Filter." Mathematical Problems in Engineering 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/3269142.

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Vehicle sideslip angle is essential for active safety control systems. This paper presents a new hybrid Kalman filter to estimate vehicle sideslip angle based on the 3-DoF nonlinear vehicle dynamic model combined with Magic Formula tire model. The hybrid Kalman filter is realized by combining square-root cubature Kalman filter (SCKF), which has quick convergence and numerical stability, with square-root cubature based receding horizon Kalman FIR filter (SCRHKF), which has robustness against model uncertainty and temporary noise. Moreover, SCKF and SCRHKF work in parallel, and the estimation outputs of two filters are merged by interacting multiple model (IMM) approach. Experimental results show the accuracy and robustness of the hybrid Kalman filter.

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Xia, Yuanqing, Zirui Xing, and Liansheng Wang. "Comparison of Several Nonlinear Filters for Mars Entry Navigation Using Radiometric Measurements." Journal of Navigation 70, no. 5 (April 24, 2017): 983–1001. http://dx.doi.org/10.1017/s0373463317000170.

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This paper studies the application of several nonlinear filters for the problem of Mars entry navigation by using radiometric measurements from Mars orbiters and Mars Surface Beacons (MSBs). A suitable dynamic model of Mars entry is developed. The movement of MSBs due to Mars rotation is also considered in the measurement model. The performance of an Extended Kalman Filter (EKF), First-order Divided Difference Filter (DDF1), Unscented Kalman Filter (UKF), and Particle Filter (PF) is compared in terms of estimation capability and computation costs. The theoretical Cramer-Rao Lower Bound (CRLB) of estimation errors are derived for Mars entry to evaluate the performance of the filters. A consistency test is also carried out to verify the filters. In simulations, by the comparison of estimation errors, position and velocity Root Mean Square Error (RMSE), error standard deviation versus Square Root of CRLB (SR CRLB), credibility and computation time, it is concluded that DDF1 is preferred for Mars entry navigation.

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Alqaisy, Mushtaq, Chandan K. Chakrabraty, Jawad K. Ali, Adam Reda Alhawari, and Tale Saeidi. "Switchable square ring bandpass to bandstop filter for ultra-wideband applications." International Journal of Microwave and Wireless Technologies 9, no. 1 (October 14, 2015): 51–60. http://dx.doi.org/10.1017/s1759078715001373.

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In this manuscript, serial-shunt of square ring resonators with step-impedance open circuited stub resonators to produce a new on-off switchable bandpass to bandstop response in the same ultra-wideband microstrip filter structure is proposed. The closed ring of series-shunt square ring resonators with a combine stubs are introduced to excite the bandpass response while bandstop characteristic excited when gaps are embedded in the corners of the square ring resonators. The main advantage of this microstrip filter is its capability to switch from bandpass-to-bandstop operation using open-short gap, respectively. A microwave simulator is utilized to show the switchable case by replacing Skyworks radio frequency diodes (RF-PIN) instead of those gaps. The entire filter models have been simulated using the computer simulation technology (CST) Microwave Studio. The computed results for the proposed filters were compared with the measured results of the both prototype structures (bandpass- and bandstop-filter). The codes also showed good agreement between them. Other advantages include being small in size, and low in effective cost.

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Kim, Pyung Soo. "Selective Finite Memory Structure Filtering Using the Chi-Square Test Statistic for Temporarily Uncertain Systems." Applied Sciences 9, no. 20 (October 11, 2019): 4257. http://dx.doi.org/10.3390/app9204257.

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In this paper, a finite memory structure (FMS) filtering with two kinds of measurement windows is proposed using the chi-square test statistic to cover nominal systems as well as temporarily uncertain systems. First, the simple matrix form for the FMS filter is developed from the conditional density of the current state given finite past measurements. Then, one of the two FMS filters, the primary FMS filter or the secondary FMS filter, with different measurement windows is operated selectively according to the presence or absence of uncertainty, to obtain a valid estimate. The primary FMS filter is selected for the nominal system and the secondary FMS filter is selected for the temporarily uncertain system, respectively. A declaration rule is defined to indicate the presence or absence of uncertainty, operate the suitable one from two filters, and then obtain the valid filtered estimate. A test variable for the declaration rule is developed using a chi-square test statistic from the estimation error and compared to a precomputed threshold. In order to verify the proposed selective FMS filtering and compare with the existing FMS filter and the infinite memory structure (IMS) filter, computer simulations are performed for a selection of dynamic systems including a F404 gas turbine aircraft engine and an electric motor. Simulation results confirm that the proposed selective FMS filtering works well for nominal systems as well as temporarily uncertain systems. In addition, the proposed selective FMS filtering is shown to be remarkably better than the IMS filtering for the temporarily uncertain system.

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Geeraert, Jeroen L., and Jay W. McMahon. "Square-Root Unscented Schmidt–Kalman Filter." Journal of Guidance, Control, and Dynamics 41, no. 1 (January 2018): 280–87. http://dx.doi.org/10.2514/1.g002921.

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Oerder, M., and H. Meyr. "Digital filter and square timing recovery." IEEE Transactions on Communications 36, no. 5 (May 1988): 605–12. http://dx.doi.org/10.1109/26.1476.

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Bhaumik, Shovan. "Square-Root Cubature-Quadrature Kalman Filter." Asian Journal of Control 16, no. 2 (April 8, 2013): 617–22. http://dx.doi.org/10.1002/asjc.704.

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Pang, Ying Zhou, Xing Yong Zhang, and Jian Tao Tian. "The SOC Estimation for Power Battery Using KF Method which Parameters are Updated by Least Square Method." Applied Mechanics and Materials 694 (November 2014): 67–72. http://dx.doi.org/10.4028/www.scientific.net/amm.694.67.

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In this article we first introduced some methods for estimating battery’s SOC and their advantages and shortcomings respectively. With experimental data, we proved that parameters of battery model are time variant. So fixed parameter Kalman Filter (FPKF) will not be suitable, then we came up with a new algorithm named adaptive Kalman Filter (APKF),which associated two algorithms—Kalman Filter and Least Square method. Kalman Filer estimates SOC of battery, while Least Square method updates parameters used in Kalman Filter. Then we used battery’s discharging data to test whether this new algorithm took effect. The results produced by Ah-counting method was viewed as a reference because of constant current discharging situation. According to the estimating results, the results produced by APKF have much smaller deviation than that produced by fixed parameters Kalman Filter (FPKF).

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26

Simandl, Miroslav, and Jindrich Duník. "SIGMA POINT GAUSSIAN SUM FILTER DESIGN USING SQUARE ROOT UNSCENTED FILTERS." IFAC Proceedings Volumes 38, no. 1 (2005): 1000–1005. http://dx.doi.org/10.3182/20050703-6-cz-1902.00168.

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Qian, Guobing, Dan Luo, and Shiyuan Wang. "A Robust Adaptive Filter for a Complex Hammerstein System." Entropy 21, no. 2 (February 9, 2019): 162. http://dx.doi.org/10.3390/e21020162.

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The Hammerstein adaptive filter using maximum correntropy criterion (MCC) has been shown to be more robust to outliers than the ones using the traditional mean square error (MSE) criterion. As there is no report on the robust Hammerstein adaptive filters in the complex domain, in this paper, we develop the robust Hammerstein adaptive filter under MCC to the complex domain, and propose the Hammerstein maximum complex correntropy criterion (HMCCC) algorithm. Thus, the new Hammerstein adaptive filter can be used to directly handle the complex-valued data. Additionally, we analyze the stability and steady-state mean square performance of HMCCC. Simulations illustrate that the proposed HMCCC algorithm is convergent in the impulsive noise environment, and achieves a higher accuracy and faster convergence speed than the Hammerstein complex least mean square (HCLMS) algorithm.

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Lian, Feng, Chen Li, Chongzhao Han, and Hui Chen. "Convergence Analysis for the SMC-MeMBer and SMC-CBMeMBer Filters." Journal of Applied Mathematics 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/584140.

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The convergence for the sequential Monte Carlo (SMC) implementations of the multitarget multi-Bernoulli (MeMBer) filter and cardinality-balanced MeMBer (CBMeMBer) filters is studied here. This paper proves that the SMC-MeMBer and SMC-CBMeMBer filters, respectively, converge to the true MeMBer and CBMeMBer filters in the mean-square sense and the corresponding bounds for the mean-square errors are given. The significance of this paper is in theory to present the convergence results of the SMC-MeMBer and SMC-CBMeMBer filters and the conditions under which the two filters satisfy mean-square convergence.

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S. Khanande, Sachin, and S. J. Honade. "Design and Implementation of Recursive Least Square Adaptive Filter Using Block DCD approach." International Journal of Reconfigurable and Embedded Systems (IJRES) 4, no. 3 (November 1, 2015): 209. http://dx.doi.org/10.11591/ijres.v4.i3.pp209-212.

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<p>Due to the explosive growth of multimedia application and tremendous demands in Very Large Scale Integrated (VLSI), there is a need of high speed and low power digital filters for digital signal processing applications. In Digital Signal Processing (DSP) systems, Finite Impulse Response (FIR) filters are one of the most common components which is used, by convolving the input data samples with the desired unit sample response of the filter. The proposed work deals with the design and implementation of RLS adaptive filter using block DCD approach. The evaluation of speed, area and power for proposed work will be done. Also, the comparison of the proposed design with the existing will be carried out for various input combinations.</p>

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ÖLMEZ, SİNEM, and UĞUR ÇAM. "REALIZATION OF SQUARE ROOT DOMAIN TOW–THOMAS BIQUADRATIC FILTER." Journal of Circuits, Systems and Computers 19, no. 05 (August 2010): 1015–24. http://dx.doi.org/10.1142/s0218126610006578.

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In this paper, a Tow–Thomas biquadratic filter designed in square root domain is proposed. The presented filter is constructed with a lossy integrator, a lossless integrator, and a summer block. To the best knowledge of the authors, the filter is the first square root domain Tow–Thomas filter in the literature. The state space synthesis method is used to design the biquadratic filter. The filter operated at 2.5 V supply voltage is simulated by using SPICE simulation program with 0.25 μm TSMC CMOS model parameters. Simulation results are in good agreement with theoretical results that the cut-off frequency and quality factor of the filter are tunable electronically.

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M., Dr Duraipandian. "Adaptive Algorithms for Signature Wavelet recognition in the Musical Sounds." Journal of Soft Computing Paradigm 2, no. 2 (May 22, 2020): 120–29. http://dx.doi.org/10.36548/jscp.2020.2.005.

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The scaling and as well as the wavelet-functions of the wavelet is detected engaging the wavelet-filters that are empowered with the filter-bank principle that is utilized in recognizing the rough calculation and the feature co-efficient of the wavelet-filter. The coefficients recognized by the filter-bank for the musical sounds produced by the musical-instruments enables one to have a signature-wavelet of the sound signal. The signature-wavelet renovates the actual musical signal with insignificant disturbance. In order to recognize the factors (coefficients) the paper employs the least mean square (L-MS), normalized least means square (NL-MS), recursive least square (R-LS) and the QR-Recursive least square (QR-RLS). Among the above four the R-LS and the QR-RLS performs well under all grounds. More over the algorithm converges swiftly compared to the other algorithm. Thus providing an accuracy and SOC (speed of convergence) improved scaling and wavelet-function recognition.

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Zemskov, Y., E. Koptseva, A. Pankratova, S. Borodulina, and S. Kalinov. "Universal prediction algorithm in maneuvering target tracking." Journal of Physics: Conference Series 2176, no. 1 (June 1, 2022): 012074. http://dx.doi.org/10.1088/1742-6596/2176/1/012074.

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Abstract The paper considers the methods to increase the accuracy of trajectory processing of the results of radar measurements in automated air traffic management systems (AATMS). The recursive filters traditionally used in the secondary processing path of radar information of modern AATMS systems are briefly considered: alpha-beta filter, linear and extended Kalman filters, multi-model filter. Along with multi-model Kalman filters it is proposed to use a universal filter based on the universal prediction theorem, the accuracy of which is asymptotically no worse than any other filter in the class of continuous functions. The algorithm for the operation of a universal alpha-beta filter was developed. As a result of modeling, it was obtained that the mean square of the tracking error of the trajectory of a maneuvering target for the universal filter during the change of the motion model turned out to be lower than for traditional filters.

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KIRCAY, ALI, M. SERHAT KESERLIOGLU, and UGUR CAM. "A NEW CURRENT-MODE SQUARE-ROOT-DOMAIN GENERAL NOTCH FILTER." Journal of Circuits, Systems and Computers 22, no. 01 (January 2013): 1250072. http://dx.doi.org/10.1142/s0218126612500727.

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In this paper, a new current-mode second-order square-root-domain general notch filter is proposed. The design is based on the state-space synthesis method with two subcircuit; square-root and squarer/divider circuits. In the circuit, the input and the output values, and dominant variables are all currents. Only MOS transistors and grounded capacitors are required to realize the filter circuit. Three cases of the second-order notch filter were obtained. The regular notch was obtained when ωn = ωp, the lowpass notch was obtained when ωn > ωp, and the highpass notch was obtained when ωn < ωp. The center frequency, and the notch frequency of the filter can be electronically tuned by changing external currents. Time and frequency domain simulations are performed using PSPICE program for the filter to verify the theory and to show the performance of it. For this purpose, the filter is simulated by using TSMC 0.35 μm Level 3 CMOS process parameters.

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M. Africa, Aaron Don, John Arvin Mercado, and Joshua Kenichi Sim. "Development of an adaptive finite impulse response filter optimization algorithm using rough set theory." Indonesian Journal of Electrical Engineering and Computer Science 31, no. 1 (July 1, 2023): 238. http://dx.doi.org/10.11591/ijeecs.v31.i1.pp238-247.

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Signal processing is crucial that as one sends information, there is a corresponding process to encode, decode, and clean the signal of unwanted noise and disruptions via use of filters. Due to the environment and how unpredictable it can be and how noise can come from almost anywhere, the typical filter to be used are adaptive filters. Adaptive filters are non-linear filters and have been used regularly regarding adaptive signal processing, this means that the filter changes accordingly and adapts to the environmental noise surrounding it. The world today has numerous applications for adaptive filters such as channel equalization and acoustic noise cancellation. This incentivizes the further development of this specific technology and the constant research that is ongoing. The main component when it comes to adaptive filtering is the algorithms used for the filter. This research compares the least mean square (LMS) and recursive least square (RLS) algorithms concerning their effectiveness in filtering out unwanted acoustic noises. The paper will cover the design and implementation of an optimized rough set based adaptive finite impulse response (FIR) filter for acoustic noise cancellation. The microstrip and bowtie antenna were used to relay the data. The software MATLAB was used for the simulation.

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Pichardo, Eduardo, Ángel Vázquez, Esteban R. Anides, Juan C. Sánchez, Hector Perez, Juan G. Avalos, and Giovanny Sánchez. "A Dual Adaptive Filter Spike-Based Hardware Architecture for Implementation of a New Active Noise Control Structure." Electronics 10, no. 16 (August 12, 2021): 1945. http://dx.doi.org/10.3390/electronics10161945.

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Presently, the technology development trend of active noise control (ANC) systems is focused on implementing advanced adaptive filters in resource-constrained electronic appliances. Recently, several authors have proved that the use of two adaptive filter algorithms significantly improves the overall adaptive filter performance. However, the computational cost of these approaches is significantly increased since they use two filters simultaneously. Consequently, these filters cannot be implemented in these devices. To solve this problem, we propose a new ANC structure with switching selection based on filtered-x normalized least mean square (FxNLMS) and filtered-x sign least mean square (FxSLMS) algorithms to reduce the computational cost of the ANC system. The improvement of this factor has allowed us to introduce for the first time an advanced spike-based architecture, which can perform dual filter operations using dynamic routing, to be used in real ANC applications. The results have demonstrated that the computational cost of the proposed dual D-FxNLMS/SLMS algorithm is lower compared with previously reported solutions.

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Ma, Run Xia, Xu Ming Zhang, Ming Yue Ding, and Qi Liu. "Comparative Study on Filter Methods of Medical Ultrasound Images." Advanced Materials Research 341-342 (September 2011): 467–71. http://dx.doi.org/10.4028/www.scientific.net/amr.341-342.467.

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This paper presents a comparative study on six despeckling methods such as modified hybrid median filter, gabor filter, speckle reducing anisotropic diffusion, homomorphic filter, non-local mean filter and squeeze box filter. We select eight objective evaluation parameters, such as signal-to-ratio, contrast signal–to–noise ratio, figure of merit, least absolute error, peak signal-to-noise ratio, edge protection factor, quantitative parameters of despeckling, signal-to-minimum mean square error ratio, to quantify the performance of these filters. The comparative study will provide a good guidance for selecting a suitable filter in the ultrasound image processing.

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Krstic, Ivan. "Design of allpass-based IIR multi-notch filters with identical pole radiuses." Serbian Journal of Electrical Engineering 20, no. 1 (2023): 1–11. http://dx.doi.org/10.2298/sjee2301001k.

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A design method for the allpass-based infinite impulse response multi-notch filters with identical pole radiuses is derived in the paper. According to the standard procedure when design of the allpass-based filters is considered, the multi-notch filters? magnitude response specifications are first formulated as the phase response specifications of the corresponding allpass filter. Then, for the specified identical pole radiuses, it is shown that unknown allpass filter coefficients can be obtained determined from the square system of linear equations. On the other hand, the minimum value of the pole radius, such that specifications of the the magnitude response are satisfied in all passbands, can be determined using the bisection method. Results of comparison with some of the existing design methods lead to the conclusion that proposed filters have higher area under the squared passbands magnitude response compared to filters with the same maximum pole radius. Furthermore, utilization of the proposed method can result in transfer functions that have the lowest possible maximum pole radius.

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Prasetya, Budi, Yuyun Siti Rohmah, Dwi Andi Nurmantris, Sarah Mulyawati, and Reza Dipayana. "Band pass filter comparison of Hairpin line and square open-loop resonator method for digital TV community." Bulletin of Electrical Engineering and Informatics 10, no. 1 (February 1, 2021): 101–10. http://dx.doi.org/10.11591/eei.v10i1.2003.

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The selection of the right filter design method is a very important first step for a radio frequency engineer. This paper presents the comparison of two methods of band pass filter design using hairpin-line and square open-loop resonator. Both methods were applied to obtain filter designs that can work for broadcasting system in digital television community. Band pass filter was simulated using design software and fabricated using epoxy FR-4 substrate. The results of simulation and measurement shown return loss value at 27.3 dB for hairpin line band pass filter and 25.901 for square open-loop resonator band pass filter. Voltage standing wave ratio parameter values were 1.09 and 1.1067 for hairpin line and square open-loop band pass filter respectively. The insertion loss values for the Hairpin line band pass filter and square open-loop band pass filter were 0.9692 and near 0 dB, respectively. Fractional bandwidth, for hairpin line band pass filter, was 6.7% while for square open-loop band pass filter was 4.8%. Regarding the size, the dimension of square open-loop resonator was approximately five times larger than hairpin-line band pass filter. Based on the advantages of the hairpin line method, we recommend that researchers choose the filter for digital TV broadcasting.

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Hu, Jian Wang, Peng Zhou, Hao Xie, Le Luo, and Hou Bo He. "Maneuvering Target Tracking Algorithm Based on IMMSCKF." Applied Mechanics and Materials 419 (October 2013): 145–50. http://dx.doi.org/10.4028/www.scientific.net/amm.419.145.

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Aiming at the tracking filters are liable to diverge and the tracking precision is low when tracking nonlinear maneuvering target, an Interacting Multiple Model Square-root Cubature Kalman Filter (IMMSCKF) is developed by introducing Square-root Cubature Kalman Filter (SCKF) into Interacting Multiple Model (IMM). This method uses SCKF for filtering each model, the weighted sum of the outputs of all parallel SCKF is taken as the output of IMMSCKF. Simulation shows that IMMSCKF has higher precision, quicker model switching speed, and smaller calculation cost compared with IMMUKF.

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Zhao, Snunyi, Yuriy Shmaliy, and Sanowar Khan. "Embedded Unbiasedness: Effect on Optimal FIR Filtering Estimates." EQUATIONS 1 (August 16, 2021): 55–61. http://dx.doi.org/10.37394/232021.2021.1.8.

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In this paper, we give an analysis of the embedded unbiasedness (EU) on optimal finite impulse response (OFIR) estimates. By minimizing the mean square error (MSE) constrained by the unbiasedness condition, a new OFIR-EU filter is derived. We show that the OFIR-EU filter does not require the initial conditions, and occupies an intermediate place between the UFIR and OFIR filters. It is also shown that the MSEs of the OFIR-EU and OFIR filters diminish with the estimation horizon. A numerical example has demonstrated that the OFIR-UE filter has better robustness against temporary model uncertainties than the OFIR and Kalman filters.

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Mu, Jing, and Chang Yuan Wang. "Iterated Cubature Kalman Filter for State Estimation of Maneuver Reentry Vehicle." Advanced Materials Research 466-467 (February 2012): 1329–33. http://dx.doi.org/10.4028/www.scientific.net/amr.466-467.1329.

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We present the new filters named iterated cubature Kalman filter (ICKF). The ICKF is implemented easily and involves the iterate process for fully exploiting the latest measurement in the measurement update so as to achieve the high accuracy of state estimation We apply the ICKF to state estimation for maneuver reentry vehicle. Simulation results indicate ICKF outperforms over the unscented Kalman filter and square root cubature Kalman filter in state estimation accuracy.

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WANG, Cheng-xi, Yi-an LIU, and Qiang ZHANG. "Improved least mean square adaptive filter algorithm." Journal of Computer Applications 32, no. 7 (August 27, 2013): 2078–81. http://dx.doi.org/10.3724/sp.j.1087.2012.02078.

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43

Buhagiar, David, and Mirna Džamonja. "Square compactness and the filter extension property." Fundamenta Mathematicae 252, no. 3 (2021): 325–42. http://dx.doi.org/10.4064/fm787-4-2020.

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De La Cruz-Blas, C. A., A. J. López-Martín, and A. Carlosena. "1.5 V tunable Square-Root Domain filter." Electronics Letters 40, no. 4 (2004): 213. http://dx.doi.org/10.1049/el:20040171.

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Zhang, Lei, Sheng Li, Enze Zhang, Qingwei Chen, and Jian Guo. "Improved square root adaptive cubature Kalman filter." IET Signal Processing 13, no. 7 (September 2019): 641–49. http://dx.doi.org/10.1049/iet-spr.2018.5029.

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46

Pavcnik, Dusan, Barry T. Uchida, Frederick S. Keller, Christopher L. Corless, and Josef Rösch. "Retrievable IVC square stent filter: Experimental study." CardioVascular and Interventional Radiology 22, no. 3 (May 1999): 239–45. http://dx.doi.org/10.1007/s002709900374.

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47

Lei, Jing, Peter Bickel, and Chris Snyder. "Comparison of Ensemble Kalman Filters under Non-Gaussianity." Monthly Weather Review 138, no. 4 (April 1, 2010): 1293–306. http://dx.doi.org/10.1175/2009mwr3133.1.

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Abstract Recently various versions of ensemble Kalman filters (EnKFs) have been proposed and studied. This work concerns, in a mathematically rigorous manner, the relative performance of two major versions of EnKF when the forecast ensemble is non-Gaussian. The approach is based on the stability of the filtering methods against small model violations, using the expected squared L2 distance as a measure of the deviation between the updated distributions. Analytical and experimental results suggest that both stochastic and deterministic EnKFs are sensitive to the violation of the Gaussian assumption, while the stochastic filter is relatively more stable than the deterministic filter under certain circumstances, especially when there are wild outliers. These results not only agree with previous empirical studies, but also suggest a natural choice of a free parameter in the square root Kalman filter algorithm.

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Chen, Jing, Chang Yin Liu, and Xue Ping Li. "The Design and FPGA Implementation of a Polyphase SRRC FIR Filter in DTMB." Advanced Materials Research 791-793 (September 2013): 2122–26. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.2122.

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Polyphase FIR filters are applied in many practical Digital Signal Processing applications where the sampling rate needs to be changed. This paper focuses on the implementation of polyphase square root raised cosine (SRRC) FIR filter based on Field Programmable Gate Array (FPGA). The filter employs methods like filter's multiphase structure, symmetrical coefficients, I/Q channel multiplexing, pipeline addition and so on to design the SRRC filter. Compared with the traditional method, the designed FIR filter exhibits the advantages of high response speed and low hardware resource s consumption.

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Duarte Júnior, José Garibaldi, Valdemir Praxedes da Silva Neto, and Adaildo Gomes d’Assunção. "A new tunable bandstop filter square-ring resonator using varactor diodes." PLOS ONE 18, no. 9 (September 1, 2023): e0290979. http://dx.doi.org/10.1371/journal.pone.0290979.

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This work presents the development of a bandstop filter with a tunable response. Varactor diodes are used as control elements. Studies and investigations demonstrate the influence of the variable capacitance on the input admittance and on the S-parameters frequency responses of the proposed square-ring resonator geometry. The design of the square-ring resonator is based on mathematical modeling of ideal transmission lines, considering parameters of characteristic admittance and electrical length for odd and even excitation modes. Based on S-parameters in ports, an equivalent circuit model of the resonator geometry is presented. The corresponding results are compared with numerical simulations. Comparative analyses are presented in order to guide the process of optimizing the physical dimensions of the layout. A prototype with dimension 0.0272 λg2 was designed, fabricated, and tested. As a measured result, a filter with two rejection bands was obtained, the first at 0.6–1.15 GHz and the second at 1.71–2.28 GHz, with 63.0 and 29.0% tuning range, respectively. In comparison with bandstop filters from the literature, the proposed reconfigurable filter presents a larger tuning range for the first band, sufficient inband rejection levels for several applications, and reduced physical dimensions. The proposed configuration is an attractive reconfigurable filtering device for use in modern communication systems operating below 3.0 GHz.

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Kircay, Ali, M. Serhat Keserlioglu, and F. Zuhal Adalar. "Electronically Tunable Current-Mode Third-Order Square-Root-Domain Filter Design." Journal of Circuits, Systems and Computers 27, no. 09 (April 26, 2018): 1850136. http://dx.doi.org/10.1142/s0218126618501360.

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In this study, electronically-tunable, current-mode, square-root-domain, third-order low-pass filter is proposed. The study is carried out with three circuit designs. First circuit is third-order low-pass Butterworth filter, second circuit is third-order low-pass Chebyshev filter and the last circuit is third-order low-pass elliptic filter. All the input and output values of the filter circuit are current. Only grounded capacitors and MOSFETs are required in order to realize the filter circuit. Additionally, natural frequency [Formula: see text] of the current-mode filter can be adjusted electronically using outer current sources. To validate the theory and to demonstrate the performance of third-order filter, frequency and time domain simulations of PSPICE program are used. To that end, TSMC 0.35[Formula: see text][Formula: see text]m Level 3 CMOS process parameters are utilized to realize the simulations of the filter.

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Journal articles on the topic 'SQUARE FILTER'

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