Fast Calculation of the Lomb-Scargle Periodogram Using Graphics Processing Units

I introduce a new code for fast calculation of the Lomb-Scargle periodogram, that leverages the computing power of graphics processing units (GPUs). After establishing a background to the newly emergent field of GPU computing, I discuss the code design and narrate key parts of its source. Benchmarking calculations indicate no significant differences in accuracy compared to an equivalent CPU-based code. However, the differences in performance are pronounced; running on a low-end GPU, the code can match 8 CPU cores, and on a high-end GPU it is faster by a factor approaching thirty. Applications of the code include analysis of long photometric time series obtained by ongoing satellite missions and upcoming ground-based monitoring facilities; and Monte-Carlo simulation of periodogram statistical properties.Comment: Accepted by ApJ. Accompanying program source (updated since acceptance) can be downloaded from http://www.astro.wisc.edu/~townsend/resource/download/code/culsp.tar.g

Beamforming Techniques for Large-N Aperture Arrays

Beamforming is central to the processing function of all phased arrays and becomes particularly challenging with a large number of antenna element (e.g. >100,000). The ability to beamform efficiently with reasonable power requirements is discussed in this paper. Whilst the most appropriate beamforming technology will change over time due to semiconductor and processing developments, we present a hierarchical structure which is technology agnostic and describe both Radio-Frequency (RF) and digital hierarchical beamforming approaches. We present implementations of both RF and digital beamforming systems on two antenna array demonstrators, namely the Electronic Multi Beam Radio Astronomy ConcEpt (EMBRACE) and the dualpolarisation all-digital array (2-PAD). This paper will compare and contrast both digital and analogue implementations without considering the deep system design of these arrays.Comment: 8 pages, Accepted IEEE Phased Array 201

High Lundquist Number Simulations of Parker\u27s Model of Coronal Heating: Scaling and Current Sheet Statistics Using Heterogeneous Computing Architectures

Parker\u27s model [Parker, Astrophys. J., 174, 499 (1972)] is one of the most discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results for a 2D version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state [Ng and Bhattacharjee, Astrophys. J., 675, 899 (2008)]. Our numerical work has now been extended to 3D using high resolution MHD numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal heating rates. Simulations are done for different values of the Lundquist number to determine scaling. In the high-Lundquist number limit (S \u3e 1000), the coronal heating rate obtained is consistent with a trend that is independent of the Lundquist number, as predicted by previous analysis and 2D simulations. We will present scaling analysis showing that when the dissipation time is comparable or larger than the correlation time of the random footpoint motion, the heating rate tends to become independent of Lundquist number, and that the magnetic energy production is also reduced significantly. We also present a comprehensive reprogramming of our simulation code to run on NVidia graphics processing units using the Compute Unified Device Architecture (CUDA) and report code performance on several large scale heterogenous machines

On Polynomial Multiplication in Chebyshev Basis

In a recent paper Lima, Panario and Wang have provided a new method to multiply polynomials in Chebyshev basis which aims at reducing the total number of multiplication when polynomials have small degree. Their idea is to use Karatsuba's multiplication scheme to improve upon the naive method but without being able to get rid of its quadratic complexity. In this paper, we extend their result by providing a reduction scheme which allows to multiply polynomial in Chebyshev basis by using algorithms from the monomial basis case and therefore get the same asymptotic complexity estimate. Our reduction allows to use any of these algorithms without converting polynomials input to monomial basis which therefore provide a more direct reduction scheme then the one using conversions. We also demonstrate that our reduction is efficient in practice, and even outperform the performance of the best known algorithm for Chebyshev basis when polynomials have large degree. Finally, we demonstrate a linear time equivalence between the polynomial multiplication problem under monomial basis and under Chebyshev basis

Synthetic Aperture Radar (SAR) data processing

The available and optimal methods for generating SAR imagery for NASA applications were identified. The SAR image quality and data processing requirements associated with these applications were studied. Mathematical operations and algorithms required to process sensor data into SAR imagery were defined. The architecture of SAR image formation processors was discussed, and technology necessary to implement the SAR data processors used in both general purpose and dedicated imaging systems was addressed

The SFXC software correlator for Very Long Baseline Interferometry: Algorithms and Implementation

In this paper a description is given of the SFXC software correlator, developed and maintained at the Joint Institute for VLBI in Europe (JIVE). The software is designed to run on generic Linux-based computing clusters. The correlation algorithm is explained in detail, as are some of the novel modes that software correlation has enabled, such as wide-field VLBI imaging through the use of multiple phase centres and pulsar gating and binning. This is followed by an overview of the software architecture. Finally, the performance of the correlator as a function of number of CPU cores, telescopes and spectral channels is shown.Comment: Accepted by Experimental Astronom

High-resolution wide-band Fast Fourier Transform spectrometers

We describe the performance of our latest generations of sensitive wide-band high-resolution digital Fast Fourier Transform Spectrometer (FFTS). Their design, optimized for a wide range of radio astronomical applications, is presented. Developed for operation with the GREAT far infrared heterodyne spectrometer on-board SOFIA, the eXtended bandwidth FFTS (XFFTS) offers a high instantaneous bandwidth of 2.5 GHz with 88.5 kHz spectral resolution and has been in routine operation during SOFIA's Basic Science since July 2011. We discuss the advanced field programmable gate array (FPGA) signal processing pipeline, with an optimized multi-tap polyphase filter bank algorithm that provides a nearly loss-less time-to-frequency data conversion with significantly reduced frequency scallop and fast sidelobe fall-off. Our digital spectrometers have been proven to be extremely reliable and robust, even under the harsh environmental conditions of an airborne observatory, with Allan-variance stability times of several 1000 seconds. An enhancement of the present 2.5 GHz XFFTS will duplicate the number of spectral channels (64k), offering spectroscopy with even better resolution during Cycle 1 observations.Comment: Accepted for publication in A&A (SOFIA/GREAT special issue