This study reports on the design of small footprint, integrated polarization filters based on engineered photonic lattices. Using a rods-in-air lattice as a basis for a TE filter and a holes-in-slab lattice for the analogous TM filter, we are able to maximize the degree of polarization of the output beams up to 98% with a transmission efficiency greater than 75%. The proposed designs allow not ...

Two novel adaptive notch filters are presented. The updating algorithms are based on the Steiglitz-McBride error criterion minimization and the basic realizations of the notch filters are all-pass based lattice filters. The proposed realizations represent an extension of a previous ad-hoc scheme for adaptive notch filtering and avoid finding the roots of a high order polynomial to obtain the un...

An Mth-order adaptive lattice filter automatically generates all M of the outputs that would be provided by M separate transversal filters. This feature can effectively suppress the narrow-band interference (NBI) of time-varying bandwidth in direct-sequence (DS) spread-spectrum systems for which the order of the interference rejection filter that achieves the optimal performance is unknown and ...

Abstract—Traditional space-time adaptive processing (STAP) algorithm not only have a big computation, but also cannot suppress the multiple narrowband jammer and the narrowband jammer which come from the same direction with the useful signal. Focus on these problems, an improved GPS anti-jam multistage nested Wiener filter (MSNWF) method which combines with multistage IIR lattice notch filter w...

Filters of a lattice, maximal filters (ultrafilters), operation to create a filter generating by an element or by a nonempty set of elements of the lattice are discussed. Besides, there are introduced implicative lattices such that for every two elements there is an element being pseudo-complement of them. Some facts concerning these concepts are presented too, i.e. for any proper filter there ...

Filters of a lattice, maximal filters (ultrafilters), operation to create a filter generating by an element or by a non-empty subset of the lattice are discussed. Besides, there are introduced implicative lattices such that for every two elements there is an element being pseudo-complement of them. Some facts concerning these concepts are presented too, i.e. for any proper filter there exists a...

We study the Medvedev degrees of mass problems with distinguished topological properties, such as denseness, closedness, or discreteness. We investigate the sublattices generated by these degrees; the prime ideal generated by the dense degrees and its complement, a prime filter; the filter generated by the nonzero closed degrees and the filter generated by the nonzero discrete degrees. We give ...

In this paper, we present a method of approximating a given 2D filter using the orthogonal wavelet filter banks. Construction of 2D orthogonal wavelet filter banks is still an open problem. In this paper, a family of orthogonal wavelet filter banks based on 2D lattice structure are used to approximate the desirable filter. By virtue of this structure, we approximate the given filter step by ste...

A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices. Define...

The stochastic gradient adaptive lattice filter is pipelined by the application of relaxed look-ahead. This form of look-ahead maintains the functional behavior of the algorithm instead of the input-output mapping and is suitable for pipelining adaptive filters. The sum and product relaxations are employed to pipeline the adaptive lattice filter. The hardware complexity of the proposed pipeline...