6,440 research outputs found
A new and efficient method for the computation of Legendre coefficients
An efficient procedure for the computation of the coefficients of Legendre
expansions is here presented. We prove that the Legendre coefficients
associated with a function f(x) can be represented as the Fourier coefficients
of an Abel-type transform of f(x). The computation of N Legendre coefficients
can then be performed in O(N log N) operations with a single Fast Fourier
Transform of the Abel-type transform of f(x).Comment: 5 page
Spectral methods in general relativistic astrophysics
We present spectral methods developed in our group to solve three-dimensional
partial differential equations. The emphasis is put on equations arising from
astrophysical problems in the framework of general relativity.Comment: 51 pages, elsart (Elsevier Preprint), 19 PostScript figures,
submitted to Journal of Computational & Applied Mathematic
Correcting soft errors online in fast fourier transform
While many algorithm-based fault tolerance (ABFT) schemes have been proposed to detect soft errors offline in the fast Fourier transform (FFT) after computation finishes, none of the existing ABFT schemes detect soft errors online before the computation finishes. This paper presents an online ABFT scheme for FFT so that soft errors can be detected online and the corrupted computation can be terminated in a much more timely manner. We also extend our scheme to tolerate both arithmetic errors and memory errors, develop strategies to reduce its fault tolerance overhead and improve its numerical stability and fault coverage, and finally incorporate it into the widely used FFTW library - one of the today's fastest FFT software implementations. Experimental results demonstrate that: (1) the proposed online ABFT scheme introduces much lower overhead than the existing offline ABFT schemes; (2) it detects errors in a much more timely manner; and (3) it also has higher numerical stability and better fault coverage
Wavemoth -- Fast spherical harmonic transforms by butterfly matrix compression
We present Wavemoth, an experimental open source code for computing scalar
spherical harmonic transforms (SHTs). Such transforms are ubiquitous in
astronomical data analysis. Our code performs substantially better than
existing publicly available codes due to improvements on two fronts. First, the
computational core is made more efficient by using small amounts of precomputed
data, as well as paying attention to CPU instruction pipelining and cache
usage. Second, Wavemoth makes use of a fast and numerically stable algorithm
based on compressing a set of linear operators in a precomputation step. The
resulting SHT scales as O(L^2 (log L)^2) for the resolution range of practical
interest, where L denotes the spherical harmonic truncation degree. For low and
medium-range resolutions, Wavemoth tends to be twice as fast as libpsht, which
is the current state of the art implementation for the HEALPix grid. At the
resolution of the Planck experiment, L ~ 4000, Wavemoth is between three and
six times faster than libpsht, depending on the computer architecture and the
required precision. Due to the experimental nature of the project, only
spherical harmonic synthesis is currently supported, although adding support or
spherical harmonic analysis should be trivial.Comment: 13 pages, 6 figures, accepted by ApJ
Non-parametric linear time-invariant system identification by discrete wavelet transforms
We describe the use of the discrete wavelet transform (DWT) for non-parametric linear time-invariant system identification. Identification is achieved by using a test excitation to the system under test (SUT) that also acts as the analyzing function for the DWT of the SUT's output, so as to recover the impulse response. The method uses as excitation any signal that gives an orthogonal inner product in the DWT at some step size (that cannot be 1). We favor wavelet scaling coefficients as excitations, with a step size of 2. However, the system impulse or frequency response can then only be estimated at half the available number of points of the sampled output sequence, introducing a multirate problem that means we have to 'oversample' the SUT output. The method has several advantages over existing techniques, e.g., it uses a simple, easy to generate excitation, and avoids the singularity problems and the (unbounded) accumulation of round-off errors that can occur with standard techniques. In extensive simulations, identification of a variety of finite and infinite impulse response systems is shown to be considerably better than with conventional system identification methods.Department of Computin
Spectral methods for CFD
One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched
On-board demux/demod
To make satellite channels cost competitive with optical cables, the use of small, inexpensive earth stations with reduced antenna size and high powered amplifier (HPA) power will be needed. This will necessitate the use of high e.i.r.p. and gain-to-noise temperature ratio (G/T) multibeam satellites. For a multibeam satellite, onboard switching is required in order to maintain the needed connectivity between beams. This switching function can be realized by either an receive frequency (RF) or a baseband unit. The baseband switching approach has the additional advantage of decoupling the up-link and down-link, thus enabling rate and format conversion as well as improving the link performance. A baseband switching satellite requires the demultiplexing and demodulation of the up-link carriers before they can be switched to their assigned down-link beams. Principles of operation, design and implementation issues of such an onboard demultiplexer/demodulator (bulk demodulator) that was recently built at COMSAT Labs. are discussed
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