Degree Of Aliasing Research Articles

PSR B0943+10: low-frequency study of subpulse periodicity in the Bright mode with LOFAR

We use broadband sensitive LOFAR observations in the 25–80 MHz frequency range to study the single-pulse emission properties of the mode-switching pulsar B0943+10. We review the derivation of magnetospheric geometry, originally based on low-frequency radio data, and show that the geometry is less strongly constrained than previously thought. This may be used to help explain the large fractional amplitudes of the observed thermal X-ray pulsations from the polar cap, which contradicted the almost aligned rotator model of PSR B0943+10. We analyse the properties of drifting subpulses in the Bright mode and report on the short-scale (minutes) variations of the drift period. We searched for the periodic amplitude modulation of drifting subpulses, which is a vital argument for constraining several important system parameters: the degree of aliasing, the orientation of the line-of-sight vector with respect to magnetic and spin axes, the angular velocity of the carousel, and thus, the gradient of the accelerating potential in the polar gap. The periodic amplitude modulation was not detected, indicating that it may be a rare or narrow-band phenomenon. Based on our non-detection and review of the available literature, we chose to leave the aliasing order unconstrained and derived the number of sparks under different assumptions about the aliasing order and geometry angles. Contrary to the previous findings, we did not find a large (of the order of 10%) gradual variation of the separation between subpulses throughout Bright mode. We speculate that this large variation of subpulse separation may be due to the incorrect accounting for the curvature of the line of sight within the on-pulse window. Finally, we report on the frequency-dependent drift phase delay, which is similar to the delay reported previously for PSR B0809+74. We provide a quantitative explanation of the observed frequency-dependent drift phase delay within the carousel model.

Supercell technique for total-energy calculations of finite charged and polar systems

We study the behavior of total-energy supercell calculations for dipolar molecules and charged clusters. Using a cutoff Coulomb interaction within the framework of a plane-wave basis set formalism, with all other aspects of the method (pseudopotentials, basis set, exchange-correlation functional) unchanged, we are able to assess directly the interaction effects present in the supercell technique. We find that the supercell method gives structures and energies in almost total agreement with the results of calculations for finite systems, even for molecules with large dipole moments. We also show that the performance of finite-grid calculations can be improved by allowing a degree of aliasing in the Hartree energy, and by using a reciprocal space definition of the cutoff Coulomb interaction.

Ray-bound tracing for perfect and efficient anti-aliasing

A complete detection of whether aliasing occurs in a given pixel is possible by using the concept of bounded rays and raybound tracing. A coherent set of rays can be bounded by bounding both their origins (by a sphere) and directions (by a circle on a unit sphere). By tracing bounds of rays in a pixel, along the direction of reflection, refraction or to light sources, it is possible to obtain an upper bound on the degree of aliasing in the pixel. Ray bound tracing is possible against various shapes and with various shading algorithms.

Stability of an algorithm to restore continuously sampled band-limited images from aliased data

A continuously sampled object is one periodically set to zero. A continuously sampled band-limited object can be restored by multiplying by an appropriately parameterized periodic function and filtering the product. The sensitivity of this restoration procedure to additive noise is considered. In general, the restoration noise level increases dramatically as the degree of aliasing of the data increases or the duty cycle of the degradation decreases. Numerical results are given for white noise and noise with Laplace autocorrelation. The results are compared with the noise sensitivity of conventional (discrete) Shannon-sampling-theorem interpolation, in which fewer data are used.