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Fast
Algorithms for Digital Signal Processing
We are seeking an
efficient algorithmic implementation of very
large, one-dimensional, cyclic convolutions
in multiprocessor or distributed
computational environments. Certain
algorithms, such as the Agarwal-Cooley
cyclic convolution algorithm, transform the
circulant matrix in a block circulant matrix
but is rather restrictive regarding the
condition imposed to the length of the
sequences. There are also other techniques
in which a one-dimensional convolution can
be performed by means of a multidimensional
convolution. The problem is that the number
of points in each dimension has to be
doubled by zero padding. We have found,
however, that if the length of the sequences
is composite (no need for the factors to be
mutually prime) the circulant matrix can be
factored into a block
pseudocirculant matrix. Each block is
circulant in itself and amenable to be
independently processed. We would like to
gain further insight into this algorithm and
to explore its multiprocessor or distributed
implementation.
Using
Synthetic Aperture Radar (SAR) to Study
Internal Packets of Solitary Waves in the
Oceans
The
internal wave packet’s phase speed, wave
amplitude, wavelength, directional wave
spectra and water column properties are
being studied based on measurements made
from the SAR images and on the knowledge of
the local bathymetry and historical
climatological data.
To support the ongoing numerical modeling of
this phenomenon a new model, recently made
available to the scientific community,
termed the Dnoidal model is being tested to
describe the evolution of internal wave
packets in the ocean.
The ability to infer interior properties of
the ocean based on the study of the surface
signature of internal solitary waves,
obtained from satellite (Synthetic Aperture
Radar) sensors, provides a powerful research
tool for extensive monitoring of large
portions of the earth oceans.
This
work is being pursued in collaboration with
the Naval Research Laboratory at
Stennis
Space
Center
. Dr.Teixeira has worked as a NAVY-ASEE
Summer Faculty Research Fellow during the
summer of 2000, was later invited as a
visiting scientist during November 2000 and
worked again as a research fellow during the
summer of 2001. This collaborative effort is
ongoing and it is expected to continue well
into the future.
A
Long-Lead Forecast Model for the Prediction
of Shelf Water Oscillations along the
Caribbean
Coast
of the
Island
of
Puerto
Rico
The Puerto Rico Seiche Forecast Model
(PRSFM), which was recently developed as a
by-product of ONR- supported research,
consists of linear and non-linear seasonal
predictors using uncorrelated harmonic
constituents. It has been proposed that
distantly originated packets of solitary
waves impinging against the shelf slope
could force the conspicuous one-hour shelf
water oscillations at the south coast of the
island
of
Puerto Rico
. This study, however, suggests that the
internal waves, if any, responsible for the
forcing of this phenomenon are more likely
to be generated at nearby locations, closer
to the south coast. The model will
facilitate the establishment of an adequate
data collection schedule for the study of
these events. Improved understanding of, and
ability to accurately predict, coastal
process with the aid of long lead forecast
models should directly bear issue on port
operations, amphibious warfare, search and
rescue and other related subjects. In
addition, coastal processes have a
definitive impact on regional shelf
ecosystems, including coral reefs, and the
surrounding environment. Notwithstanding
that these kind of coastal water
oscillations are usually considered quite
unpredictable, in a continuous six-month
period this predictor accounted for up to
70% of the low frequency variability of the
seiche. The research and further development
of this model is an ongoing project.
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