Efficient sampling of band-limited signals from sine wave crossings

This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing timings, which are then used to interpolate the input signal at arbitrary instants. Potentially, it may allow for reductions in power consumption and complexity in these converters. The reconstruction in the discrete domain is based on a recently-proposed modification of the Lagrange interpolator, which is readily implementable with linear complexity and efficiently, given that it re-uses known schemes for variable fractional-delay (VFD) filters. As a spin-off, the method allows one to perform spectral analysis from sine wave crossings with the complexity of the FFT. Finally, the results in the correspondence are validated in several numerical examples.

The outburst decay of the low magnetic field magnetar SWIFT J1822.3−1606: phase-resolved analysis and evidence for a variable cyclotron feature

We study the timing and spectral properties of the low-magnetic field, transient magnetar SWIFT J1822.3−1606 as it approached quiescence. We coherently phase-connect the observations over a time-span of ∼500 d since the discovery of SWIFT J1822.3−1606 following the Swift-Burst Alert Telescope (BAT) trigger on 2011 July 14, and carried out a detailed pulse phase spectroscopy along the outburst decay. We follow the spectral evolution of different pulse phase intervals and find a phase and energy-variable spectral feature, which we interpret as proton cyclotron resonant scattering of soft photon from currents circulating in a strong (≳1014 G) small-scale component of the magnetic field near the neutron star surface, superimposed to the much weaker (∼3 × 1013 G) magnetic field. We discuss also the implications of the pulse-resolved spectral analysis for the emission regions on the surface of the cooling magnetar.