Abstract In this paper, the notions of maximal GE-filter and prime a GE-algebra are introduced relation between them is given. Some characterizations GE-filters transitive given in terms generated by subset GE-algebra. We generalized Stone’s theorem to GE-algebras. The notion elitable bordered investigated its properties. observed that class all complete distributive lattice. Equivalent conditi...

This paper presents a current-mode 64 × 1 early vision chip, including integrated photodiodes and a programmable “perceptual engine”, which can implement various perceptual algorithms, such as Gabor filters. The proposed chip can be used for early vision tasks as edge detection, texture analysis, depth estimation and motion analysis. The perceptual engine exploits the properties of MOS transist...

In this paper, we present a new structure for linear−phase filter banks without redundancy, which have unequal−length filters at each subband. First, we extend the simplified lattice structure of the linear−phase filter bank to the unequal−length linear−phase paraunitary filter bank. In general, the unequal−length linear−phase paraunitary filter bank has equal−length filters at both the analysi...

Anticausal or time-reversed inversion of digital filters has gained importance in recent years in the implementation of digital filter banks. Anticausal inversion has, in the past, been shown to be possible by using block processing with appropriate state initialization. With (A, B , C , D) denoting the state space description of a structure implementing a filter G(z), the anticausal inverse ca...

Classical filter design is typically based on the assumption that the cost is proportional to the filter order. Here we revisit this assumption and show that is may be advantageous to instead use filter structures that have low sensitivity to element errors. We first discuss the mechanism behind the low sensitivity of doubly resistively terminated lossless networks and estimated of the passband...

A (distributive) p-algebra is an algebra 〈L;∨,∧, ∗, 0, 1〉 whose reduct 〈L;∨,∧, 0, 1〉 is a bounded (distributive) lattice and whose unary operation ∗ is characterized by x ≤ a if and only if a ∧ x = 0. If L is a p-algebra, B(L) = { x ∈ L : x = x } and D(L) = { x ∈ L : x = 1 } then 〈B(L);∪,∧, 0, 1〉 is a Boolean algebra when a ∪ b is defined to be (a∗ ∧ b∗)∗, for any a, b ∈ B(L), D∗(L) = { x ∨ x∗ ...

In order to research the logical system whose propositional value is given in a lattice from the semantic viewpoint, Xu [7] proposed the concept of lattice implication algebras, and discussed some of their properties. Xu and Qin [8] introduced the notion of implicative filters in a lattice implication algebra, and investigated some of their properties. Turunen [5] introduced the notion of Boole...

Here, we propose an add-drop and a channel drop filter based on two-dimensional photonic crystal all circular ring resonators. These structures are made of a square lattice of silicon rods with the refractive index n1=3.464 surrounded by air (with refractive index n2=1). The broadest photonic band gap occurs at the filling ratio of r/a = 0.17. Two linear defect W1 waveguides couple to the ring....

Photonic crystal ring resonators (PCRRs) are traditional structures fordesigning optical channel drop filters. In this paper, Photonic crystal channel drop filter(CDFs) with a new configuration of ring resonator is presented. The structure is made ofa square lattice of silicon rods with the refractive index nsi=3. 4 which are perforated inair with refractive index nair=1. Calculations of band s...

The rest of the paper is organized as follows: in Section 1, we give preliminary definitions of relevant terms and notation; in Section 2, we formally define the permutohedral lattice in several ways and prove useful structural properties stemming from the definition; in Section 3, we suggest criteria for picking the ideal lattice with which to perform Gaussian filtering, and present an argumen...