Partitioning filters

In this paper a fundamentally new and computationally attractive class of linear filters—the partitioned filters—are presented and their important properties are briefly discussed. Specifically, it is shown that the partitioned filters constitute a powerful and unifying framework for linear estimation, posses a naturally parallel-processing structure, and yield numerically effective, robust, and fast estimation algorithms. As such, the partitioned filters constitute attractive alternatives to previous estimation algorithms such as the Kalman filter.     

Efficient synthesis of gaussian filters by cascaded uniform filters

Gaussian filtering is an important tool in image processing and computer vision. In this paper we discuss the background of Gaussian filtering and look at some methods for implementing it. Consideration of the central limit theorem suggests using a cascade of ``simple' filters as a means of computing Gaussian filters. Among ``simple' filters, uniform-coefficient finite-impulse-response digital filters are especially economical to implement. The idea of cascaded uniform filters has been around for a while [13], [16]. We show that this method is economical to implement, has good filtering characteristics, and is appropriate for hardware implementation. We point out an equivalence to one of Burt's methods [1], [3] under certain circumstances. As an extension, we describe an approach to implementing a Gaussian Pyramid which requires approximately two addition operations per pixel, per level, per dimension. We examine tradeoffs in choosing an algorithm for Gaussian filtering, and finally discuss an implementation.     

Boolean filters and positive implicative filters of residuated lattices

The aim of this paper is to introduce the notions of Boolean filters and positive implicative filters in residuated lattices and to investigate their properties. Several characterizations of Boolean filters and positive implicative filters are derived. The extension theorems of implicative filters and positive implicative filters are obtained. The relations among Boolean filters, implicative filters and positive implicative filters are investigated and it is proved that Boolean filters are equivalent to implicative filters, and that every Boolean filter is a positive implicative filter, but the converse may not be true. Furthermore, the conditions under which a positive implicative filter is a Boolean filter are established.     

Range filters: Localintensity subrange filters and their properties

A local filter which uses the local-intensity subrange of pixel intensity values within a window is described. The range filter is an extension of the rank filter and has been found useful for detecting edges. The deterministic and noise properties of the range filter are described and compared with those of the commonly used Sobel filter.     

From special analogous crystal filters to digital impacting filters

The implementation of high-speed and high-efficiency wireless communications, or Ultra Narrow Band (UNB) modulation, depends on the design of a special digital filter, which needs to not only maintain or even enlarge the minute differences in modulated waveforms, but also weaken noise or interference. This paper proposes a novel but simple digital impacting filter produced by exploiting the mechanism of zero group delay crystal filters. The proposed filter can cooperate with the usual small-angle modulation of UNB modulation, especially with Extended Binary Phase Shift Keying (EBPSK) modulation, which can convert the signal characteristics in noise into high-amplitude impacting at the phase jump points, such that the UNB signal is easy to detect. A computer simulation illustrates the validity of the proposed filter.     

格的模糊滤子与模糊素滤子的度量

主要研究了模糊代数中格的模糊（素）滤子的度量。首先给出了模糊（素）滤子度的新概念,并利用模糊（素）滤子度讨论了格的模糊子集是模糊（素）滤子的程度。其次,利用格的模糊集的（强）水平集得到了模糊（素）滤子的等价刻画。最后,讨论了任意多个模糊子集的交、直积的模糊（素）滤子度以及格的模糊子集在同态映射下像与原像的模糊（素）滤子度的性质。     

Microprocessor-based signal filters

The concepts of microprocessor-based signal filters are presented via a case study of a simple low-pass filter designed using the bilinear z-transform method. The paper provides a general introduction to signal filtering using microprocessor-based forms of implementation, and discusses several alternative system configurations based on commercially available microprocessors or special purpose integrated circuits.     

Multirate digital filters

This paper provides a review of recent developments in multirate digital filters and attempts to fill a long existing gap between multirate digital filters and multirate sampled-data feedback control systems.     

Adaptive multi-dimensional filters

In the present work, adaptive multi-dimensional filtering technique is proposed, which in addition to numerical stabilization, results in significant reduction of computational efforts. A criterion for adaptive filtering is proposed with algorithm provided. A new buffer domain technique based on adaptive filtering is developed and demonstrated for flow past a stationary cylinder for different Reynolds numbers. This technique also allows calculations in a reduced domain, showing another use of adaptive filtering. Rotary oscillation of a circular cylinder at different forcing parameters show excellent match with results in the literature, demonstrating potential benefits of adaptive filtering.     

量子计算与量子计算机

量子计算的强大运算能力使得量子计算机具有广阔的应用前景。该文简要介绍了量子计算的发展现状和基本原理,列举了典型的量子算法,阐明了量子计算机的优越性,最后预测了量子计算及量子计算机的应用方向。     

量子测量与量子计算

本文的讨论主要集中在量子力学中测量部分,首先从量子力学的几大公设出发,着重分析测量公设的含义。然后提出量子力学争论的焦点问题之一——测量问题,并通过分别阐述塌缩原理、非塌缩原理以及对二者的比较来分析各种说法的合理性。接下来简要讨论同时测量问题。最后简略描述测量在不同量子计算模型中的体现,并对测量带来的问题做了思考。     

量子纠缠和量子计算

量子纠缠是量子力学中的一种非经典现象。本文从介绍纠缠和纠缠态出发,着重讨论纠缠的本质和非定域性概念。文末还讨论了纠缠在量子计算中的作用：它是量子计算优于经典计算的重要原因之一。     

FI代数的模糊素MP滤子与模糊超MP滤子

将Zadeh提出的模糊集概念应用于FI代数,提出了FI代数的模糊素MP滤子和模糊超MP滤子的概念并研究其性质及相互关系。给出了满足一定条件的并半格FI代数的模糊素MP滤子的若干等价刻画并建立了模糊素MP滤子定理。获得了一个模糊集成为超模糊MP滤子的充要条件。     

Optimal mean-square N-observation digital morphological filters: I. Optimal binary filters

The present paper places binary morphological filtering into the framework of statistical estimation, the intent being to develop the theory of mean-square (MS) optimization. Classical binary morphological operations are interpreted as numerical functionals on binary N-vectors, so that in the random setting they can be treated as estimators dependent on N binary observation random variables. For single-erosion filters, optimization is achieved by finding the structuring element that minimizes MS error. Using the Matheron representation as a guide, we generalize the analysis to morphological filters given by unions of multiple erosions and optimize by minimizing MS error over all collections of erosions, or over a prefixed number of erosions. In all cases, MS error is relative to the estimation of an unobserved variable by a morphological function of observed variables. A key element in the method is use of the basis form of the Matheron expansion to reduce significantly the structuring-element search. The technique is adapted to special morphological filters by constraining the basis representation in accordance with the class of interest. It is demonstrated that optimization in terms of erosions is equivalent to optimization in terms of dilations.     

Mixture ensemble Kalman filters

A generic algorithmic framework for nonlinear ensemble filtering based on Gaussian mixtures and fuzzy clustering techniques is introduced. The framework generalizes the ensemble Kalman filter and relaxes the assumption of a Gaussian prediction distribution. A theoretical analysis of the proposed procedure is provided, establishing strong consistency under suitable assumptions. Specific implementations are discussed and adjustments that are necessary in high-dimensional settings are proposed. A simple implementation of the filter is shown to work well in common testbeds, providing substantial gains over the ensemble Kalman filter.     

Simplex-directed partitioned adaptive filters

A new combination of mathematical programming methods and partitioned adaptive filters is proposed for the simultaneous real-time estimation of the parameters and state of an unknown linear system. The algorithm uses a version of the simplex method of non-linear programming to direct parameter selection for a bank of Kidman filters, thus combining the known convergence characteristics of partitioned adaptive filters with the robustness of this search technique. Motivation for the approach is discussed in light of recently published results concerning convergence of the decision function of the partitioned filters, and a simple example is given.     

Approximations to unsupervised filters

The problem of recursive estimation of an additive noise-corrupted discrete stochastic process is considered for the case where there is a nonzero probability that the observation does not contain the process. Specifically, it is assumed that, independently, with unknown, constant probabilities, observations consist either of pure noise, or derive from a discrete linear process, and that the true source of any individual observation is never known. The optimal Bayesian solution to this unsupervised learning problem is unfortunately infeasible in practice, due to an ever increasing computer time and memory requirement, and computationally feasible approximations are necessary. In this correspondence a quasi-Bayes (QB) form of approximation is proposed and comparisons are made with the well-known decision-directed (DD) and probabilistic-teacher (PT) schemes.     

Almost periodic all-pass filters

A definition for a linear system with almost periodic coefficients to define an all-pass filter is proposed and a condition for such system to be all-pass is obtained.     

Redefined fuzzy implicative filters

Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (θ, ψ)-fuzzy implicative filters where θ, ψ are any two of {∈, q, ∈ ∨ q, ∈ ∧ q} with θ ≠ ∈ ∧ q is introduced, and related properties are discussed. Relations between (∈ ∨ q, ∈ ∨ q)-fuzzy implicative filters and (∈, ∈ ∨ q)-fuzzy implicative filters are investigated, and conditions for an (∈, ∈ ∨ q)-fuzzy implicative filter to be an (∈, ∈)-fuzzy implicative filter are provided. Characterizations of (∈, ∈ ∨ q)-fuzzy implicative filters are given, and conditions for a fuzzy set to be a (q, ∈ ∨ q)-fuzzy implicative filter are provided.