Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for DCTs and DSTs

This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives the algorithms by stepwise decomposition of the associated signal models, or polynomial algebras. This decomposition is based on two generic methods or algebraic principles that generalize the well-known Cooley-Tukey FFT and make the algorithms' derivations concise and transparent. Application to the 16 discrete cosine and sine transforms yields a large class of fast algorithms, many of which have not been found before.Comment: 31 pages, more information at http://www.ece.cmu.edu/~smar

Comparison of in situ aerosol measurements with SAGE 2 and SAM 2 aerosol measurements during the airborne Antarctic ozone experiment

Models indicate that stratospheric aerosols play a major role in the destruction of ozone during the Austral winter. Although many in situ measurements of stratospheric aerosols were made during the Airborne Antarctic Ozone Experiment, changes of aerosol concentration and size distributions across the polar vortex are important to understanding changes of chemical species taking place during this time. Therefore comparing the in situ measurements with measurements made by satellites scanning wider areas will give a clearer picture of the possible role played by aerosols during this period. The wire impactor size distributions are compared to those from the aerosol spectrometers and a best fit size distribution determined. Aerosol extinctions are calculated from the in situ measurements and compared to the extinctions measured by the satellites. Five comparisons are made with SAGE 2 and four with SAM 2. Extinctions agree as close as a factor of two

Pair Plasma Instability in Homogeneous Magnetic Guide Fields

Pair plasmas, collections of both matter and antimatter particles of equal mass, represent a paradigm for the study of basic plasma science, and many open questions exist regarding these unique systems. They are found in many astrophysical settings, such as gamma-ray bursts, and have recently also been produced in carefully designed laboratory experiments. A central research topic in plasma physics is instability; however, unlike their more common ion–electron siblings, pair plasmas are generally thought to be stable to cross field pressure gradients in homogeneous magnetic fields. It is shown here by means of kinetic full-f simulations that, when a pressure gradient is first established, the Gradient-driven Drift Coupling mode is destabilized and becomes turbulent. Force balance is eventually achieved by a combination of flattened pressure profiles due to turbulent transport and establishment of a magnetic field gradient, saturating the growth. During the unstable phase, key physics can be captured by a δf gyrokinetic description, where it is shown analytically and numerically that parallel particle motion results in a coupling of all electromagnetic field components. A fluid model derived therefrom accurately predicts linear eigenmodes and is used to resolve global profile effects. For laser-based electron–positron plasma experiments, prompt instability is predicted with growth times much shorter than plasma lifetimes. Similarly, growth rates are calculated for the planned APEX experiment as well as gamma-ray burst scenarios, suggesting that the instability may contribute to the early evolution of these systems.</p