In this paper, we show how novel recursive formulations of block pseudocirculant matrices lead to a new class of parallel cyclic convolution algorithms that exhibit a high degree of regularity and modularity and are suitable for parallel or pipelined implementation into today's very large scale integration (VLSI) circuits, multifield-programmable gate arrays (multi-FPGAs) systems, and multiprocessor architectures. In addition to the architectural advantages, the proposed formulations offer a comparable number of parallel subsections, and a reduction in the number of pre/postprocessing vector operations, for the same range of decimation rates proposed by the most efficient alternative algorithm. The proposed algorithms do not impose any of the traditional constraints, such as the demand that the convolution length be factorable into mutually prime factors. The use of recursion results in the definition of two new mathematical constructs, which are intrinsic to these novel architectures, the higher order block pseudocirculant or superblock pseudocirculant matrix and the block pseudocyclic shift operator that leads to unfolded data-flow graphs of cyclic shifts.Index Terms-Block pseudocirculants, cyclic shift, fast convolution, higher order block pseudocirculants, parallel cyclic convolution, superblock pseudocirculant matrices, unfolded cyclic shift operators.
[1] This study is in an area south of the Shandong peninsula, near the region where Zhou et al. (1991) observed anomalous drops in acoustical intensity. Solitary wave generation and propagation simulations are performed using the Lamb (1994) nonhydrostatic model. The model simulations show that, for summer conditions, the existing semi-diurnal tidal flow over the topographic variations formed internal bores and solitary waves. For the Shandong area, we analyzed summer observations from Synthetic Aperture Radar (SAR) that tracked solitary wave trains from their surface roughness signatures. The images contained seven events consisting of internal bores and solitary waves that traveled in a well-defined direction for 2.5 days. The origin of the trains appeared at a well-defined point along a steep topographic drop. The SAR observations guided and tuned the model simulations, by comparing spectra of observed and modeled wavelengths. The tuned model yields wavelengths within factors of 2, or less, of those derived from SAR data. Wavelength and amplitude dispersion analysis showed two dispersion regimes. Modeled phase speeds were at the lower limit of phase speeds deduced from SAR data, from about 0.8 to 1.0 m/s. Acoustical intensity calculations in the presence of solitary wave trains will be undertaken in a subsequent paper using a parabolic equation acoustical model along the path of solitary wave train propagation.
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