The goal of this project is to invert electroencephalogram data to brain activity using a novel and accurate algorithm. This algorithm can be used for research and development of brain-machine interfaces, potentially to include prosthetic control, surveillance and lie detection. This report details the mathematical and physical theory behind the algorithm developed during this effort. The algorithm is novel in that it does not use the quasistatic approximation throughout the ...
An algorithm is introduced for the rapid evaluation at appropriately chosen nodes on the two-dimensional sphere S(exp 2) in R(exp 3) of functions specified by their spherical harmonic expansions (known as the inverse spherical harmonic transform), and for the evaluation of the coefficients in spherical harmonic expansions of functions specified by their values at appropriately chosen points on S(exp 2) (known as the forward spherical harmonic transform). The procedure is ...
The main accomplishments during this grant period are in the following areas: (1) Fast parallel algorithms for Legendre and spherical transforms. The accomplishments in this area effectively break down into two subareas, namely: (a) Development of fast algorithms for the discrete Legendre transform (FLT). (b) Development of factorizations of the Fourier transform (FFT) and the cosine transform (FCT) adapted for the use in spherical transforms. (2) Fast N-body algorithms. (3) ...
Steven Rizk is involved in continuing the work that was proposed under the AASERT program. First, he has worked on developing the Vector Spherical Harmonic (VSH) model by including it in a WWW interface that can be accessed easily from any web browser. Second, he developed a set of interfaces that enabled us to compare the VSH model with radar data Mr. C. Bunto has been developing a version of ...
First differences of magnetic observatory monthly means for 1963-1982 were analyzed using techniques of spherical harmonic analysis and power spectral analysis. The external source signal is shown to be primarily zonal in geomagnetic coordinates. Prominent peaks are present in the power spectrum at frequencies of 1.0 cycle/yr and 2.0 cycles/yr. The annual signal is largest on the degree 2 external zonal spherical harmonic, while the semiannual signal is largest on ...
Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based near-side observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two ...
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*SPHERICAL HARMONICS
