Signal Reconstruction via H-infinity Sampled-Data Control Theory: Beyond the Shannon Paradigm

This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter. The proposed H-infinity performance criterion naturally takes intersample behavior into account, reflecting the energy distributions of the signal. We present methods for computing optimal solutions which are guaranteed to be stable and causal. Detailed comparisons to alternative methods are provided. We discuss some applications in sound and image reconstruction

Structural and dynamical uncertainties in modeling axisymmetric elliptical galaxies

Quantitative dynamical models of galaxies require deprojecting the observed surface brightness to determine the luminosity density of the galaxy. Existing deprojection methods for axisymmetric galaxies assume that a unique deprojection exists for any given inclination, even though the projected density is known to be degenerate to the addition of "konus densities" that are invisible in projection. We develop a deprojection method based on linear regularization that can explore the range of luminosity densities statistically consistent with an observed surface brightness distribution. The luminosity density is poorly constrained at modest inclinations (i > ~30 deg), even in the limit of vanishing observational errors. In constant mass-to-light ratio, axisymmetric, two-integral dynamical models, the uncertainties in the luminosity density result in large uncertainties in the meridional plane velocities. However, the projected line-of-sight velocities show variations comparable to current typical observational uncertainties.Comment: 20 pages, 8 Postscript figures, LaTeX, aaspp4.sty, submitted to MNRAS; paper w/figs (600 kb) also available at http://cfa-www.harvard.edu/~romanow/ell.mn.ps.gz GIF-format figures replaced by PostScrip

X-ray reverberation around accreting black holes

Luminous accreting stellar mass and supermassive black holes produce power-law continuum X-ray emission from a compact central corona. Reverberation time lags occur due to light travel time-delays between changes in the direct coronal emission and corresponding variations in its reflection from the accretion flow. Reverberation is detectable using light curves made in different X-ray energy bands, since the direct and reflected components have different spectral shapes. Larger, lower frequency, lags are also seen and are identified with propagation of fluctuations through the accretion flow and associated corona. We review the evidence for X-ray reverberation in active galactic nuclei and black hole X-ray binaries, showing how it can be best measured and how it may be modelled. The timescales and energy-dependence of the high frequency reverberation lags show that much of the signal is originating from very close to the black hole in some objects, within a few gravitational radii of the event horizon. We consider how these signals can be studied in the future to carry out X-ray reverberation mapping of the regions closest to black holes.Comment: 72 pages, 32 figures. Accepted for publication in The Astronomy and Astrophysics Review. Corrected for mostly minor typos, but in particular errors are corrected in the denominators of the covariance and rms spectrum error equations (Eqn. 14 and 15