In this paper, a novel orthogonal 2-D lattice structure is incorporated into the design of a nonseparable 2-D fourchannel perfect reconstruction filter bank. The proposed filter bank is obtained by using the polyphase decomposition technique which requires the design of an orthogonal 2-D lattice filter. Due to constraint of perfect reconstruction, each stage of this lattice filter bank is simpl...

We have designed a new type of optical channel drop filter (CDF) based on two dimensionaltriangular lattice photonic crystals. CDF operation is based on coupling to the photonic crystalwaveguide. The proposed structure is optimized to work as a CDF for obtaining the CDFcharacteristics and band structure of the filter the finite difference time domain (FDTD) method andplane wave expansion (PWE) ...

Here, we propose an optical filter and an optical power splitter based on two-dimensionalphotonic crystal all circular ring resonators. These structures are made of a square lattice ofsilicon rods with the refractive index n1=3.464 surrounded by air (with refractive indexn2=1). First, we have designed the filter and by using that, we designed a power splitter. Thetransmission efficiency and Qua...

The notion of stratified (L, M)-semiuniform convergence tower spaces is introduced, which extends the notions ofprobabilistic semiuniform convergence spaces and lattice-valued semiuniform convergence spaces. The resulting categoryis shown to be a strong topological universe. Besides, the relations between our category and that of stratified (L, M)-filter tower spaces are studied.

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

This paper presents the behavior of reflection coefficients of a stochastic gradient lattice (SGL) filter applied to a codedivision multiple-access overlay system. Analytic expressions for coefficients for a two-stage filter are derived in a Rayleigh fading channel with the presence of narrow-band interference and additive white Gaussian noise. It is shown that the coefficients of the lattice f...

We investigate a special class of N-channel oversampled linearphase perfect reconstruction filter banks with a smaller decimation factor M than N. We deal with systems in which all analysis and synthesis filters have the same FIR length and share the same center of symmetry. We provide the general lattice factorization of a polyphase matrix of a particular class of these oversampled filter bank...

Ahstpact-Convergence properties of a continuously adaptive digital lattice filter. used as a linear predictor are investigated for both an unnormalized and a normalized gradient adaptation algorithm. The PARCOR coefficient mean values and the output mean-square error (MSE) are approximated and a simple model is described which approximates these quantities as functions of time. Calculated curve...

At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...