Linear phase paraunitary filter banks: theory, factorizations and designs

M channel maximally decimated filter banks have been used in the past to decompose signals into subbands. The theory of perfect-reconstruction filter banks has also been studied extensively. Nonparaunitary systems with linear phase filters have also been designed. In this paper, we study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase. Specific instances of this problem have been addressed by other authors, and linear phase paraunitary systems have been shown to exist. This property is often desirable for several applications, particularly in image processing. We begin by answering several theoretical questions pertaining to linear phase paraunitary systems. Next, we develop a minimal factorizdion for a large class of such systems. This factorization will be proved to be complete for even M. Further, we structurally impose the additional condition that the filters satisfy pairwise mirror-image symmetry in the frequency domain. This significantly reduces the number of parameters to be optimized in the design process. We then demonstrate the use of these filter banks in the generation of M-band orthonormal wavelets. Several design examples are also given to validate the theory

On the Redshift Distribution of Gamma Ray Bursts in the Swift Era

A simple physical model for long-duration gamma ray bursts (GRBs) is used to fit the redshift (z) and the jet opening-angle distributions measured with earlier GRB missions and with Swift. The effect of different sensitivities for GRB triggering is sufficient to explain the difference in the z distributions of the pre-Swift and Swift samples, with mean redshifts of ~1.5 and ~2.7, respectively. Assuming that the emission properties of GRBs do not change with time, we find that the data can only be fitted if the comoving rate-density of GRB sources exhibits positive evolution to z >~ 3-5. The mean intrinsic beaming factor of GRBs is found to range from ~34-42, with the Swift average opening half-angle ~10 degree, compared to the pre-Swift average of ~7 degree. Within the uniform jet model, the GRB luminosity function is proportional to L^{-3.25}_*, as inferred from our best fit to the opening angle distribution. Because of the unlikely detection of several GRBs with z <~ 0.25, our analysis indicates that low redshift GRBs represent a different population of GRBs than those detected at higher redshifts. Neglecting possible metallicity effects on GRB host galaxies, we find that ~1 GRB occurs every 600,000 yrs in a local L_* spiral galaxy like the Milky Way. The fraction of high-redshift GRBs is estimated at 8-12% and 2.5-6% at z >= 5 and z >= 7, respectively, assuming continued positive evolution of the GRB rate density to high redshifts.Comment: Accepted for publication in ApJ. The paper contains 29 pages and 24 figure

Thiotepa hyperpigmentation preceding epidermal necrosis: malignant intertrigo misdiagnosed as Stevens-Johnson syndrome-toxic epidermal necrolysis overlap

Thiotepa is a common alkylating agent known to precipitate cutaneous reactions consistent with toxic erythema of chemotherapy, including erythema and hyperpigmentation. Herein, we describe an atypical case of malignant intertrigo involving preferential erythema and desquamation not only of skin folds but also of occluded areas after thiotepa-based conditioning. The diagnosis was complicated by concurrent stomatitis and oral petechiae in the setting of autologous stem cell transplant 11 days prior for diffuse large B-cell lymphoma. Histopathological examination from two cutaneous sites demonstrated epidermal dysmaturation and eccrine gland necrosis consistent with thiotepa-induced desquamation and not Stevens-Johnson syndrome or graft-versus-host-disease. Malignant intertrigo can present with extensive cutaneous involvement, as evidenced by our patient who had 25% body surface area affected. Mucosal involvement is common with most chemotherapeutic regimens and its presence should not deter the astute clinician from consideration of a diagnosis of toxic erythema of chemotherapy. No further interventions were needed and the patient healed spontaneously

Long-range Ni/Mn structural order in epitaxial double perovskite La2NiMnO6 thin films

We report and compare the structural, magnetic, and optical properties of ordered La2NiMnO6 thin films and its disordered LaNi0.5Mn0.5O3 counterpart. An x-ray diffraction study reveals that the B-site Ni/Mn ordering induces additional XRD reflections as the crystal symmetry is transformed from a pseudocubic perovskite unit cell in the disordered phase to a monoclinic form with larger lattice parameters for the ordered phase. Polarized Raman spectroscopy studies reveal that the ordered samples are characterized by additional phonon excitations that are absent in the disordered phase. The appearance of these additional phonon excitations is interpreted as the clearest signature of Brillouin zone folding as a result of the long-range Ni/Mn ordering in La2NiMnO6. Both ordered and disordered materials display a single ferromagnetic-to-paramagnetic transition. The ordered films display also a saturation magnetization close to 4.8 mB/f.u. and a transition temperature (FM-TC) around 270 K, while the disordered ones have only a 3.7 mB/f.u. saturation magnetization and a FM-TC around 138 K. The differences in their magnetic behaviours are understood based on the distinct local electronic configurations of their Ni/Mn cations.Comment: 15 pages, 5 fig

Phase formation, phonon behavior, and magnetic properties of novel ferromagnetic La3BAlMnO9 (B = Co or Ni) triple perovskites

In the quest for novel magnetoelectric materials, we have grown, stabilized and explored the properties of La3BAlMnO9 (B = Co or Mn) thin films. In this paper, we report the influence of the growth parameters that promote B/Al/Mn ordering in the pseudo-cubic unit cell and their likely influence on the magnetic and multiferroic properties. The temperature dependence of the magnetization shows that La3CoAlMnO9 is ferromagnetic up to 190 K while La3NiAlMnO9 shows a TC of 130 K. The behavior of these films are compared and contrasted with related La2BMnO6 double perovskites. It is observed that the insertion of AlO6 octahedra between CoO6 and MnO6 suppresses significantly the strength of the superexchange interaction, spin-phonon and spin-polar coupling.Comment: 13 pages, 3 fig

Influence of Ni/Mn cation order on the spin-phonon coupling in multifunctional La2NiMnO6 epitaxial films by polarized Raman spectroscopy

We report the influence of Ni/Mn ordering on the spin-phonon coupling in multifunctional La2NiMnO6. Three types of films with different levels of structural order, including long-range Ni/Mn cation order, cation disorder, and an admixture of the ordered and disordered phases, are compared by polarized micro-Raman spectroscopy and magnetometry. Each film displays a strong dependence on the polarization configuration and a unique set of Raman active phonon excitations. Long-range cation ordering results in the splitting of Raman active phonon peaks because of Brillouin zone folding and lowering symmetry. Phonon mode softening begins clearly at a distinct temperature for each sample revealing a strong spin-lattice interaction. It follows closely the magnetization curve in ordered films. Unlike the admixture and the ordered films, softening behavior is strongly suppressed in the cation-disordered films. These differences may be understood based on the variation in amplitude of the spin-spin correlation functions due to the local Ni/Mn cation ordering.Comment: 17 pages, 7 fig

Investigation of phonon behavior in Pr2NiMnO6 by micro-Raman spectroscopy

The temperature dependence of phonon excitations and the presence of spin phonon coupling in polycrystalline Pr2NiMnO6 samples were studied using micro-Raman spectroscopy and magnetometry. Magnetic properties show a single ferromagnetic-to-paramagnetic transition at 228 K and a saturation magnetization close to 4.95 \muB/f.u.. Three distinct Raman modes at 657, 642, and 511 cm-1 are observed. The phonon excitations show a clear hardening due to anharmonicity from 300 K down to 10 K. Further, temperature dependence of the 657 cm-1 mode shows only a small softening. This reflects the presence of a relatively weak spin-phonon coupling in Pr2NiMnO6 contrary to other double perovskites previously studied.Comment: 10 pages, 4 fig