Lattice Filter Research Articles

Distance functions and filter topological residuated lattices1

In this paper, we firstly extend C. C. chang’s distance functions from MV-algebras into residuated lattices. But in general, the functions may not be a distance function on residuated lattices. We introduce weak involutory residuated lattices, in which Chang’s function is a pseduo distance function. Moreover we prove that the functions become distance functions on involutory residuated lattices. Secondly by use of the function and a lattice filter, we define F-ball on residuated lattices, and we prove that the set of all F-balls forms a base of a topology τLF on an involutory residuated lattice. Moreover we show that the topology τLF on an involutory residuated lattice L makes L to be a topological residuated lattice. At last, we use filters instead of lattice filters to set up filter topologies on an involutory residuated lattice, and study the properties of the filter topologies.

Pure copper extrusion additive manufacturing of lattice structures for enabling enhanced thermal efficiency in hydrogen production

The high geometrical complexity allowed by Additive Manufacturing (AM) of pure copper can support the development of more efficient catalytic supports that can enable the design of efficient reactors for key processes for energy transition, i.e., hydrogen production with methane steam reforming or CO2 conversion to synthetic methane, thanks to the enhanced thermal conductivity of the catalytic support. Low relative density lattice geometries with open cell copper geometries can be adopted as catalyst supports in the new generation chemical reactors to improve the heat transfer. This work presents a manufacturability study about pure copper lattice filters produced via metal Extrusion AM i.e., via feedstock 3D printing and sintering. The results show that feasible parts design can be reached and produced and that heat-exchange performances can be increased with respect to conventional supports, as confirmed by lab-scale heat transfer tests. A specific metrological assessment based on CTscan data is implemented on the printed parts to qualify them and to ensure a good thermal coupling between the printed filters and the heat exchanger main tube elements.

Broadband near-infrared emission in silicon waveguides

Silicon photonic integrated circuit foundries enable wafer-level fabrication of entire electro-optic systems-on-a-chip for applications ranging from datacommunication to lidar to chemical sensing. However, silicon’s indirect bandgap has so far prevented its use as an on-chip optical source for these systems. Here, we describe a fullyintegrated broadband silicon waveguide light source fabricated in a state-of-the-art 300-mm foundry. A reverse-biased p-i-n diode in a silicon waveguide emits broadband near-infrared optical radiation directly into the waveguide mode, resulting in nanowatts of guided optical power from a few milliamps of electrical current. We develop a one-dimensional Planck radiation model for intraband emission from hot carriers to theoretically describe the emission. The brightness of this radiation is demonstrated by using it for broadband characterization of photonic components including Mach-Zehnder interferometers and lattice filters, and for waveguide infrared absorption spectroscopy of liquid-phase analytes. This broadband silicon-based source can be directly integrated with waveguides and photodetectors with no change to existing foundry processes and is expected to find immediate application in optical systems-on-a-chip for metrology, spectroscopy, and sensing.

Generating some large filters of quasiorder lattices

Generating some large filters of quasiorder lattices

Ultra‐Power‐Efficient, Electrically Programmable, Multi‐State Photonic Flash Memory on a Heterogeneous III‐V/Si Platform

AbstractNon‐volatile charge‐trap flash memory (CTM) co‐located with heterogeneous III‐V/Si photonics is demonstrated. The wafer‐bonded III‐V/Si CTM cell facilitates non‐volatile optical functionality for a variety of devices such as Mach–Zehnder Interferometers (MZIs), asymmetric MZI lattice filters, and ring resonator filters. The MZI CTM exhibits full write/erase operation (100 cycles with 500 states) with wavelength shifts of Δλnon‐volatile = 1.16 nm (Δneff,non‐volatile ≈ 2.5 × 10−4) and a dynamic power consumption <20 pW (limited by measurement). Multi‐bit write operation (2 bits) is also demonstrated and verified over a time duration of 24 h and most likely beyond. The cascaded second order ring resonator CTM filter exhibited an improved ER of ≈7.11 dB compared to the MZI and wavelength shifts of Δλnon‐volatile = 0.041 nm (Δneff, non‐volatile = 1.5 × 10−4) with similar pW‐level dynamic power consumption as the MZI CTM. The ability to co‐locate photonic computing elements and non‐volatile memory provides an attractive path toward eliminating the von‐Neumann bottleneck.

$\sigma$-filters of distributive lattices

$\sigma$-filters of distributive lattices

Novel Architecture of Fir Lattice Filter with Reduced Interconnect Delay Impacts Towards Reduced Power-delay Product using Pipelining and Parallel Processing for Medical Applications

Three important parameters area, speed and power are important. In VLSI design, the speed is determined by the critical path delay. Delay is depending on the data path taken for processing in the VLSI design. By minimizing data-path delay using efficient architecture the speed of the design of system can be improved in turn to result in better performance. In this new era, data-path delay is the dominating one compared to logic delay. So, it is very essential to concentrate more towards path delay in any architecture design. Even though the speed is important it is having in trade of with power. This data-path delay can be reduced by different technique like pipelining, parallel processing, register retiming. Also, by constructing this architecture in an innovative way the power is having trade of with delay. So the power-delay product can be taken as the reduced one. In this paper, various architecture of delay-product optimized FIR filter and Lattice filter architecture is being surveyed and implemented in order to get minimum delay-power product

Computationally Efficient Poisson Time-Varying Autoregressive Models through Bayesian Lattice Filters

Estimation of time-varying autoregressive models for count-valued time series can be computationally challenging. In this direction, we propose a time-varying Poisson autoregressive (TV-Pois-AR) model that accounts for the changing intensity of the Poisson process. Our approach can capture the latent dynamics of the time series and therefore make superior forecasts. To speed up the estimation of the TV-AR process, our approach uses the Bayesian Lattice Filter. In addition, the No-U-Turn Sampler (NUTS) is used, instead of a random walk Metropolis–Hastings algorithm, to sample intensity-related parameters without a closed-form full conditional distribution. The effectiveness of our approach is evaluated through model-based and empirical simulation studies. Finally, we demonstrate the utility of the proposed model through an example of COVID-19 spread in New York State and an example of US COVID-19 hospitalization data.

Refined Fuzzy Profile Matching

A profile describes a set of properties, e.g. a set of skills a person may have or a set of skills required for a particular job. Profile matching aims to determine how well a given profile fits to a requested profile and vice versa. Fuzzyness is naturally attached to this problem. The filter-based matching theory uses filters in lattices to represent profiles, and matching values in the interval [0,1], so the lattice order refers to subsumption between the concepts in a profile. In this article the lattice is extended by additional information in form of weighted extra edges that represent partial quantifiable relationships between these concepts. This gives rise to fuzzy filters, which permit a refinement of profile matching. Another way to introduce fuzzyness is to treat profiles as fuzzy sets. In the present paper we combine these two aproaches. Extra edges may introduce directed cycles in the directed graph of the ontology, and the structure of a lattice is lost. We provide a construction grounded in formal concept analysis to extend the original lattice and remove the cycles such that matching values determined over the extended lattice are exactly those resulting from the use of fuzzy filters in case of crisp profiles. For fuzzy profiles we show how to modify the weighting construction while eliminating the directed cycles but still regaining the matching values. We also give sharp estimates for the growth of the number of vertices in this construction.

Modeling and Simulation of a Micro strip Antenna in Annular Geometry

In the last decade, the study of multidimensional systems for signal filtering purpose has attracted the attention of many research teams, which are motivated by various interesting real world applications such Image processing, video signal filtering processing, video signal filtering Computational tomography, distributed parameters systems. The representation of the state space realization for two-dimensional (2D) filters by a transfer function, with minimal delays is a crucial problem; the minimal realization can avoidmathematical complexities as well as technical benefit to hardware requirement. Unfortunately, it is not possible to find the minimal state space realization for every 2D system other than the 1D system, but we can find it for a specific cases of all-pole or the all-zero. Lattice filter is classified as an important structure in digital signal processing. In fact, it minimizes the computation complexity, reduces the finite word length and requires less hardware compared to the direct form digital filter with similar design specifications. The authors in two delay units z1-1 , z2-1 are used. In this paper we propose a new lattice-ladder structure of 2-D digital filter, composed of a delay units z1-1 and a basic lattice section z1 and z2-1 - Using matrix representation of the basic lattice sections and we derived transfer functions of the proposed 2-D digital ladder-lattice filters. The proposed structure is composed by a minimal number of delays and a minimal number of basic lattice sections. Furthermore, we have considered the description of the proposed lattice structure by using a state-space n-D Roesser form description presented in below and the implementations suggested by the authors in literatures. Besides, the state space equations for 2-D digital filter are presented, where the dimension of the matrices of the proposed lattice structure verify the minimal state space realization. The remainder of the paper is organized as follows; first is devoted to the proposed -D lattice-ladder structure and realization and in the second is dedicated to the state space realization. As conclusion this work has allowed us to approach a field that has experienced a great growth in recent years which is constantly evolving in order to improve, understanding and control the complex systems and processes that surround us.

The design and implementation of folded adaptive lattice filter structures in FPGA for ECG signals

An adaptive filter is the utmost essential filter castoff in statistical signal dealing. The fine-tuning of the filter factor in relation to the response signal is the adaptive filter's key feature due to fewer calculations, Least Mean Square (LMS) adaptive filters are widely used to remove noise from Electrocardiograms (ECG). The adaptive filters are realized as signal processing algorithms in Digital Signal Processors (DSPs) or in VLSI Signal Processors (VSPs). The technique provides a way to create a folded adaptive lattice LMS filter, which requires less hardware than an adaptive lattice filter. Folding is an algorithm that uses a time scheduling technique that combines arithmetic operations into one operation which reduces Register and silicon chip areas. The design and implementation of a folded lattice adaptive filter remove Power Line Interference (PLI) noise from ECG signals. The MATLAB Xilinx System Generator tool is used to design the Adaptive Lattice LMS Filter and Folded Adaptive Lattice LMS Filter with Folding Order K = 2 and K = 4 and realized in the Virtex 5 FPGA KIT. The results of the folded architecture show that the area is reduced for K = 2 and K = 4 by 82.60% and 91.05%, respectively compared with a normal adaptive lattice filter.

Fluid flow analysis of the lattice-based ceramic filters in molten metal filter application

The ceramic lattice filters are ideal for various technical applications, including filtration, flow stability, and heat transfer, that could alter the transport characteristics like pressure, permeability, and velocity. The authors presented a computational study based on the fluid flow parameters for four struts-based lattice structures in this work. This study includes seven designs of four struts-based lattice structures systematically created with 30 pores per inch (PPI) and 80% porosity while varying the unit cell sizes and strut diameter. The present computational study has been carried out using the turbulent k-epsilon (k-ε) model with the chosen metal alloy, IN718. The efficacy of the lattice filters has been determined by visualizing the physical parameters like pressure drop and velocity distribution patterns inside the filters. This study concludes that the BCC and the Diamond lattice structures have outperformed the other designs. Moreover, the effects of the variation in the unit cell and strut size have been evaluated for different structures and discussed.

Adaptive feedback cancellation based on interaural level difference using lattice filter with correlation control for binaural hearing devices

This paper proposes a correlation control method for linear prediction filters based on howling detection using binaural information in hearing aids. In a closed-loop system, high autocorrelation of the input signal can cause estimation errors owing to biased solutions, resulting in an acoustic artifact known as entrainment. Adaptive feedback cancellation (AFC) based on the linear prediction error method (PEM) has been successfully used as a solution to this bias. However, if the convergence speed of the linear prediction filter is faster than the estimated speed of the feedback path, removal of the feedback signal would be difficult. The proposed method uses a strategy to improve convergence by detecting howling based on the interaural level difference (ILD) and controlling the decorrelation performance of the correlation control algorithm of the adaptive lattice filter. Experimental results indicate that the adaptive filter of the proposed method significantly improves the estimation accuracy and tracking performance. The robustness of the proposed method is also confirmed via objective and subjective evaluation experiments on the generation of artifacts. Experimental results obtained using autocorrelated input signals show that the proposed method significantly improves robustness to entrainment compared to the conventional bilateral AFC method.

Bayesian circular lattice filters for computationally efficient estimation of multivariate time-varying autoregressive models

Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series. The time-varying vector autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series. Nevertheless, in most cases, the large number of parameters presented by the model results in a high computational burden, ultimately limiting its usage. To address this issue, a computationally efficient multivariate Bayesian Circular Lattice Filter is developed, extending the usage of the TV-VAR model to a broader class of high-dimensional problems. The fully Bayesian framework allows both the autoregressive (AR) coefficients and innovation covariance to vary over time. The proposed estimation method is based on the Bayesian lattice filter (BLF), which is extremely computationally efficient and stable in univariate cases. To illustrate the effectiveness of the proposed approach, a comprehensive comparison with other competing methods is conducted through simulation studies and finds that, in most cases, the proposed approach performs superior in terms of the average squared error between the estimated and true time-varying spectral density. Finally, the methodology is demonstrated through applications to quarterly Gross Domestic Product (GDP) data and Northern California wind data.

Prediction Error Method (PEM)-Based Howling Cancellation in Hearing Aids: Can We Do Better?

This work develops an effective technique acoustic feedback cancellation (AFC) in the digital hearing aid (DHAid) devices. The normalized least mean square (NLMS) algorithm-based AFC method may suffer from a biased convergence. The biased convergence problem is considerably resolved by the prediction error method (PEM)-based AFC (PEM-AFC); however, it may demonstrate a slow convergence. The proposed method’s main structure is based two adaptive filters. The main adaptive AFC filter receives its input from the DHAid receiver signal, while the auxiliary AFC filter is activated by a probe signal. The main idea is to apply a lattice filtering-based pre-processing for decorrelation in the main AFC filter’s update equation. This produces a Newton-like adaptive algorithm with fast convergence. Additionally, the lattice filtering is executed on a sample-by-sample basis, in contrast to the frame-based execution in the traditional PEM-AFC method. As the AFC system converges, the level of the probe signal is decreased to improve the output SNR; however, the low-level input signal slows down auxiliary AFC filter’s convergence. In order to improve the convergence speed, the gradient information from a maximum Versoria-criterion (MVC) is incorporated into the auxiliary AFC filter’s update algorithm. The two adaptive filters’ coefficients are exchanged, to ensure that both adaptive filters converge to a good estimate of the true acoustic feedback path. Simulations show that the proposed method works well for speech/signals and for DHAid devices with different gain settings. Additionally, the proposed method shows robust performance in the event of a sudden change in the acoustic environment.

Coaxial filters of distributive lattices

Coaxial filters of distributive lattices

Median filters of pseudocomplemented distributive lattices

Median filters of pseudocomplemented distributive lattices

Application of Neutrosophic Filters in Lattice Implication Algebra

Neutrosophic set theory is applied to lattice implication algebra, and the concept of neutrosophic filters and neutrosophic lattice filters in lattice implication algebra are introduced. Several properties are investigated. Characterizations of a neutrosophic filter are discussed. Finally, we proved that every neutrosophic filter is a neutrosophic lattice filter, but the converse is invalid.

A Signal Flow Graph Approach to the Resolution of Spherical Triangles Using CORDIC

Jack Volder’s original motivation for the COordinate DIgital Computer (CORDIC) was the real-time digital solution of spherical triangle equations employed in airborne navigation, for which he presented a solution flow diagram without detailing its construction. In fact, without a strong guidance, it is not easy to express the solutions of linear algebraic problems such as those involved when solving spherical triangles as cascades of CORDIC operations—called by Volder CORDIC solution-flow diagrams—and thus to devise a system solution on CORDIC processing units. As it gives a bird’s eye view of the system design problem, a signal flow graph representation of the underlying system of linear equations provides such guidance; the operations leading to the problem solution are uncovered by performing a sequence of partial flow reversals on the graph. The approach is illustrated by the problem where two sides and the included angle of a spherical triangle are given, called SAS problem, that is encountered in applications as diverse as air navigation, lattice filters for adaptive processing, and dexterous robotic hands. The solutions thus obtained are at least as efficient as existing ones, whenever available.

Boosters and Filters in MS-Almost Distributive Lattices

This paper deals on boosters and \(\beta\)-filters in MS-almost distributive lattice \(M\). It is proved that the set of all boosters in \(M\) is a bounded distributive lattice. Characterization of \(\beta\)-filters of $M$ in terms of boosters is established and a dual homomorphism of \(M\) and the set of all boosters of \(M\) is derived. Further, it is shown that every filter in \(M\) is an \(e\)-filter and every maximal filter in \(M\) is a \(\beta\)-filter. Equivalent conditions on which the set of all boosters is a relatively complemented lattice are established.