We present a design scheme to achieve equalization of Gaussian-like spectra by using linear-phase optical lattice filters. The proposed scheme separates the design of the phase response from the amplitude response of the equalization filter by introducing a symmetrically folded lattice structure. With the proposed structure, the linear-phase characteristic of the equalization filter is guarante...

It has been proposed that all M -channel paraunitary (PU) multirate filter banks over GF(2) can be described using the product of basic lattice blocks. In this paper this conjecture is proven by considering a redefinition of degree-0 lattice blocks. A factorisation algorithm that factors all degree-J PU filter banks over GF(2) is presented. In the course of this work M -channel type-I matrices ...

We will now dig deeper into the details of this matrix factorization, and discuss the two specific bilateral representations we use: the simplified bilateral grid, and the permutohedral lattice [1]. Filtering with both the permutohedral lattice and the simplified bilateral grid works by “splatting” a value at each pixel onto a small number of vertices, performing a separable blur in the space o...

A core technical contribution of this work is the generalization of the Gaussian permutohedral lattice convolution proposed in [1] to the full non-separable case with the ability to perform backpropagation. Although, conceptually, there are minor difference between non-Gaussian and general parameterized filters, there are non-trivial practical differences in terms of the algorithmic implementat...

We discuss the n-fold implicative/fantastic filters in lattice implication algebras, which are extended notions of implicative/fantastic filters. Characterizations of n-fold implicative/fantastic filters are given. Conditions for a filter to be n-fold implicative are provided. Extension property for an n-fold fantastic filter is established.

Our aim in this paper is to introduce and study a new sort of fuzzy sublattice (ideal, filter) of a lattice called ) q , ( ∨ ∈ ∈ -fuzzy sublattice (ideal, filter). These fuzzy sublattices (ideals, filters) are characterized by their level sublattices (ideals, filters). Finally, we give a generalization of ) q , ( ∨ ∈ ∈ -fuzzy sublattices (ideals, filters).

We characterize a fuzzy lattice through a fuzzy partial order relation, define ideals and filters of fuzzy lattices, characterize an ideal of fuzzy lattice using its level set and its support and show that a subset of a fuzzy lattice is an ideal if and only if its support is an ideal. Similarly, we show the same for its level set. Lastly, we define some kinds of ideals and filters of fuzzy latt...

In this paper, based on Hájek, Vychodil, Rachunek and Šalounová’s works, we study the concept of v-filters of residuated lattices with weak vt-operators, axiomatize very true operators, discuss filters and v-filters of residuated lattices with weak vt-operator, give the formulas for calculating the v-filters generated by subsets, and show that lattice of v-filters of a commutative residuated la...

A multirate IF filter for mobile radio has been implemented in silicon. The filter consists of a decimation stage followed by a bandpass filter. Both parts use a lattice wave digital structure. The design and implementation are described beginning with the filter specification and proceed through algorithmic design, operations scheduling, and resource allocation and assignment. Every step tries...

Abstract Extending the belongs to (∈) relation and quasi-coincidence with(q) relation between fuzzy points and a fuzzy subsets, the concept of (α, β)-fuzzy filters and (α, β)-fuzzy filters of lattice implication algebras are introduced, where α, β ∈ {∈h , qδ, ∈h ∨qδ, ∈h ∧qδ}, α, β ∈ {∈h, qδ, ∈h ∨ qδ, ∈h ∧ qδ} but α ∈h ∧qδ, α ∈h ∧ qδ, respectively, and some related properties are investigated. S...