Comparison between Windowed FFT and Hilbert-Huang Transform for Analyzing Time Series with Poissonian Fluctuations: A Case Study

Hilbert-Huang Transform (HHT) is a novel data analysis technique for nonlinear and non-stationary data. We present a time-frequency analysis of both simulated light curves and an X-ray burst from the X-ray burster 4U 1702-429 with both the HHT and the Windowed Fast Fourier Transform (WFFT) methods. Our results show that the HHT method has failed in all cases for light curves with Poissonian fluctuations which are typical for all photon counting instruments used in astronomy, whereas the WFFT method can sensitively detect the periodic signals in the presence of Poissonian fluctuations; the only drawback of the WFFT method is that it cannot detect sharp frequency variations accurately.

A special kind of local structure in the CMB intensity maps: duel peak structure

We study the local structure of Cosmic Microwave Background (CMB) tem- perature maps released by the Wilkinson Microwave Anisotropy Probe (WMAP) team, and find a new kind of structure, which can be described as follows: a peak (or valley) of average temperature is often followed by a peak of temperature fluctuation that is 4 ° away. This structure is important for the following reasons: both the well known cold spot detected by Cruz et al. and the hot spot detected by Vielva et al. with the same technology (the third spot in their article) have such structure; more spots that are similar to them can be found on CMB maps and they also tend to be significant cold/hot spots; if we change the 4° characteristic into an artificial one, such as 3° or 5°, there will be less "similar spots", and the temperature peaks or valleys will be less significant. The presented "sim- ilar spots" have passed a strict consistency test which requires them to be significant on at least three different CMB temperature maps. We hope that this article could arouse some interest in the relationship of average temperature with temperature fluctuation in local areas; meanwhile, we are also trying to find an explanation for it which might be important to CMB observation and theory.

Development of the super high angular resolution principle for X-ray imaging

Development of the Super High Angular Resolution Principle (SHARP) for coded-mask X-ray imaging is presented. We prove that SHARP can be considered as a generalized coded mask imaging method with a coding pattern comprised of diffraction-interference fringes in the mask pattern. The angular resolution of SHARP can be improved by detecting the fringes more precisely than the mask's element size, i.e. by using a detector with a pixel size smaller than the mask's element size. The proposed mission SHARP-X for solar X-ray observations is also briefly discussed.

A super-high angular resolution principle for coded-mask X-ray imaging beyond the diffraction limit of a single pinhole

High angular resolution X-ray imaging is always useful in astrophysics and solar physics. In principle, it can be performed by using coded-mask imaging with a very long mask-detector distance. Previously, the diffraction-interference effect was thought to degrade coded-mask imaging performance dramatically at the low energy end with its very long mask-detector distance. The diffraction-interference effect is described with numerical calculations, and the diffraction-interference cross correlation reconstruction method (DICC) is developed in order to overcome the imaging performance degradation. Based on the DICC, a super-high angular resolution principle (SHARP) for coded-mask X-ray imaging is proposed. The feasibility of coded mask imaging beyond the diffraction limit of a single pinhole is demonstrated with simulations. With the specification that the mask element size is 50 × 50 μm2 and the mask-detector distance is 50m, the achieved angular resolution is 0.32arcsec above about 10keV and 0.36arcsec at 1.24keV (λ = 1 nm), where diffraction cannot be neglected. The on-axis source location accuracy is better than 0.02 arcsec. Potential applications for solar observations and wide-field X-ray monitors are also briefly discussed.