Stability and convergence analysis of transform-domain LMS adaptive filters with second-order autoregressive process

In this paper, the stability and convergence properties of the class of transform-domain least mean square (LMS) adaptive filters with second-order autoregressive (AR) process are investigated. It is well known that this class of adaptive filters improve convergence property of the standard LMS adaptive filters by applying the fixed data-independent orthogonal transforms and power normalization. However, the convergence performance of this class of adaptive filters can be quite different for various input processes, and it has not been fully explored. In this paper, we first discuss the mean-square stability and steady-state performance of this class of adaptive filters. We then analyze the effects of the transforms and power normalization performed in the various adaptive filters for both first-order and second-order AR processes. We derive the input asymptotic eigenvalue distributions and make comparisons on their convergence performance. Finally, computer simulations on AR process as well as moving-average (MA) process and autoregressive-moving-average (ARMA) process are demonstrated for the support of the analytical results.

The thermal stability and structural site-distribution of Eu3+ ions in the red-emitting phosphors Ca9Eu2W4O24 and Sr9Eu2W4O24

The red-emitting phosphors Ca₉Eu₂W₄O₂₄ and Sr₉Eu₂W₄O₂₄ were synthesized by the solid-state reaction method. The crystal phases were characterized by X-ray powder diffraction. The photoluminescence excitation and emission spectra were investigated. The luminescence excitation and emission spectra confirm that the phosphors are efficiently excited by near UV light. The dependence of luminescence intensities on the heating temperatures was investigated. The Ca₉Eu₂W₄O₂₄ phosphor exhibits higher thermal stability than that of Sr₉Eu₂W₄O₂₄. The crystallographic sites for Eu³⁺ ions in Ca₉Eu₂W₄O₂₄ and Sr₉Eu₂W₄O₂₄ are investigated by the site-selective excitation spectra in the ⁵D₀ → ⁷F₀ wavelength region. It is identified that the Eu³⁺ ions occupy only M sites (statistically occupied by 0.5Eu and 0.5Ca) in Ca₉Eu₂W₄O₂₄ and, however, the Eu³⁺ ions can substitute both M sites (Eu³⁺ + Sr²⁺) and Sr²⁺ sites in Sr₉Eu₂W₄O₂₄. The luminescence spectra and the thermal stability are discussed on the basis of the crystal structure, Eu³⁺ site-distributions and the energy transfer.