Physics 640:
Scientific Computation and Visualization
Prof.
http://www.faculty.umb.edu/tomas_materdey/640
Fall ’07 Syllabus
Week 1 & 2:
-Introduction
to Matlab and the Fast Fourier Transform (FFT)
*Matlab,
FFT, noise elimination in signal processing
*Discrete-time Fourier Transform in Fortran
Project 1:
a) Write a code
to look at the real and imaginary parts of the FFT of a sum signal of two
sinusoids of different frequencies; eliminate the high frequency portion of the
spectrum, then show plots of the inverse transforms (IFFT) of the real parts
and the imaginary parts. Explain what was the difference
versus doing the inverse transform on the direct transform without separating
the real and imaginary parts.
b) Use a
low-pass filter on the spectrum of a signal with white noise added (SNR=2,
ratio of amplitudes) to recover the original signal without noise. Repeat for
SNR=1. Show with plots what did you obtain; is it important to have a minimum
number of points of the signal?
c) Write a Fortran code to do the discrete-time Fourier Transform of a
sum of two sinusoids of different frequencies. Get the output file from the
UNIX machine and show the plots using Matlab.
Links: Fortran Standard; Example of a fortran code
(FDTD2D)
Bibliography:
1.- Duhamel,
P.; Vetterli, M.: "Fast Fourier transforms: a
tutorial review and a state of the art", Signal Process. 19 (1990), no. 4, 259--299. MR91a:94004
2.- Oppenheim
and Willsky, Signals and Systems 2ed, Prentice Hall;
ISBN: 0-13-814757-4, Chapters 3-5
3.- Kamen
and Heck, Fundamentals of Signals and Systems, Prentice Hall, chapters 4 and 7
http://users.ece.gatech.edu/~bonnie/book/
4.- Wavelet Online: http://www.wavelet.org
5.- H.D. Knoble,
Fortran Resources, http://www.personal.psu.edu/faculty/h/d/hdk/fortran.html
6.- Open Directory Project, Fortran
Source Codes and More: http://www.dmoz.org/Computers/Programming/Languages/Fortran
Week 3 & 4
-Introduction
to numerical algorithms
-Finite-Difference
in the
-Finite-Difference
in the
-Implementation
of a FDTD code in Fortran:
Project 2:
a)
Develop
a Fortran code to propagate a sinusoid or a Gaussian pulse in 1D, save outputs
into a file
b)
Show
the animations using Matlab
Bilbiography:
1.-
A. Taflove and
S. C. Hagness,
Computational Electrodynamics: The
Finite-Difference Time-Domain Method, 3rd ed.
2.- D.M. Sullivan, Electromagnetic
Simulation Using the FDTD Method , IEEE Press
3.- K. S. Yee, ``Numerical solution of
initial boundary value problems involving Maxwell's equations in isotropic
media,'' IEEE Trans. Antennas Propagat.,
vol. AP-14, no. 4, pp. 302--307, 1966.
4.- A. Taflove and M. E. Brodwin,
"Numerical solution of steady-state
electromagnetic scattering problems using the
time-dependent Maxwell's equations," IEEE
Trans. Microwave Theory and
Techniques, vol. 23, pp.
623-630, Aug. 1975. (Download Paper2.pdf )
5.- A. Taflove and K. R. Umashankar,
"Solution of Complex Electromagnetic
Penetration and Scattering Problems in Unbounded
Regions," pp. 83-113 in Computational Methods for
Infinite Domain Media-Structure Interactions, American
Society of Mechanical Engineers, AMD vol. 46
(1981).
6.-V. Sathiaseelan, B. B. Mittal, A. J. Fenn, and A. Taflove, "Recent Advances in
External Electromagnetic Hyperthermia," Chap. 10 in Advances in Radiation
Therapy, B. B. Mittal, J. A. Purdy, and
K. K. Ang, eds.
(Cancer Treatment and Research,
S. T. Rosen, series ed.)
Week 5 & 6:
-Absorbing
Boundary Conditions in FDTD
Example Program
FDTD2D
Project 3:
a)
Run
and visualize results from the FDTD2D programs AND
b)
Feed
a correct mode for two parallel dielectric waveguides, observe wave
coupling OR
c)
Write
a FDTD 2D code for wave propagation in Fortran 77 as extension of Project 2,
with absorbing boundary conditions
Bibliography:
1.-D. Marcuse, Theory of Dielectric Optical Waveguides
2.-B. Engquist and A. Majda, ``Absorbing boundary conditions for the numerical
simulation of waves,'' Math. Comp., vol. 31, pp. 629--651, 1977.
3.-E. L. Lindman, ````Free-space''
boundary conditions for the time dependent wave equation,'' J. Comput. Phys., vol. 18, pp. 67--78, 1975.
4.-G. Mur, ``Absorbing boundary
conditions for the finite-difference approximation of the time-domain
electromagnetic-field equations,'' IEEE Trans. Electromagn.
Compat., vol. EMC-23, no. 4, pp.
377--382, 1981.
5.-R. L. Higdon, ``Absorbing boundary conditions for
difference approximations to the multi-dimensional wave equations,'' Math. Comput., vol. 47, no. 176, pp. 437--459,
1986.
6.-R. L. Higdon, ``Numerical absorbing boundary conditions for
the wave equation,'' Math. Comput., vol. 49, no.
179, pp. 65--90, 1987.
Week 7 & 8:
-Introduction
to Molecular Dynamics/Metropolis Algorithm/Monte Carlo
Project 4:
a)
Molecular
interactions, execute the Example Program MolDyn for several particles with different initial
conditions, is there low or high sensitivity on these conditions? Use output
files to visualize animations of particle motions using Matlab.
b)
Execute
an example program based on the Metropolis
algorithm, varying on or two parameters, present results using Matlab
Bibliography:
1.-F. Ercolessi,
A Molecular Dynamics Primer, http://www.fisica.uniud.it/~ercolessi/
2.-M. Field, A Practical Introduction to the Simulation of Molecular Systems
3.-N. Metropolis, A.W. Rosenbluth,
M.N. Rosenbluth, A.H. Teller and E. Teller, (1953) J.
Chem. Phys. 21, 1087-1092.
4.-Z.Q. Li and H.A. Scheraga,
(1987) Proc. Natl. Acad. Sci. USA 84,
6611-6615.
5.-Rasmussen, J. L. (1984). A Fortran
program for statistical evaluation of pseudorandom number generators. Behavior
Research Methods and Instrumentation, 16, 63-64.
6.-The Basics of Monte Carlo Simulations:
http://www.cs.cornell.edu/jwoller/samples/montecarlo/default.html
Week 9 & 10:
-Introduction
to time-frequency analysis: Wigner function and
wavelets
Project 5:
a)
Develop
a Matlab code that allows you to recognize a vowel from a
recording (wav file) using the Wigner transform.
b)
Write
a Matlab code to demonstrate the advantage of using
wavelet transform versus Fourier transform in signal recovery
Matlab code to calculate the Wigner function; and wavelet
subroutines will be available
Bibliography:
[1] Rabiner
and Juang, Fundamentals
of Speech Recognition, Prentice Hall, 1993
[2] Rabiner, L.R., and Levinson,
S.E., Isolated and Connected Word
Recognition –Theory and Selected Applications, IEEE Trans. Communications,
COM-29 (5), pp. 621-659, May 1981
[3] Rabiner
and Schafer, Digital Processing of Speech
Signals, Prentice Hall, 1978
[4] Atal, B.S., and Hanauer, S.L., Speech
Analysis and Synthesis by Linear Prediction of the Speech Wave, J. Acoust. Soc. Am., 50 (2), pp. 637-655, August 1971.
[5] Meeklenbrauker
and Hlawatsch, The
Wigner Distribution, Elsevier, 1997
[6] Wigner,
E.P., Phys. Rev. 40, pp.749-759,
1932
[7] Cohen, L., Time-Frequency Analysis, Prentice Hall,
1995
[8] Allen, J.B., Application of Short-Time Fourier Transform
to Speech Processing and Spectral Analysis, IEEE Int. Conf. On Acoustics,
Speech and Sig. Proc., pp 1012-1015, Paris, France, May 1982
[9] Boashash,B., Note on the Use of the Wigner
Distribution for
[10] Bouachache,B.,
and Rodriguez, F., Recognition of
Time-Varying Signals in the Time-Frequency Domain by Means of the Wigner Function, IEEE Int. Conf. On Acoustics, Speech,
and Sig. Proc., pp. 2251-2254, San Diego, CA, 1984
[11] Materdey, T. and Seyler, C., Int. J. Modern Physics B, vol. 17,
no. 25, 4555 (2003)
[12] Materdey, T. and Seyler, C., Int. J. Modern Physics B, vol. 17,
no. 26, 4683 (2003)
[13] Materdey, T. The Wigner
Function as a Voice Identification Tool, Interactive Demo, IEEE Vis 2002,
[14] Rumelhart, D.E.
and McCleland, J.L., eds., Parallel Distributed Processing: Learning Internal Representations by
Error Propagations,
[15] Sejnowski,
T.J., and
[16] Mitchell, P., Fortran-77 Neural Network Simulator (F77NNS) User Guide, Cosmic
program #MSC-21638, National Aeronautics and Space Administration, 1987
[17] Lippmann, R., An Introduction to Computing with Neural
Nets, IEEE ASSP Mag., 4 (2), pp. 4-22, April
1987.
[18] Weibel, A., Hanazawa, T., Hinton, G., Shikano,
K., Lang, K.J., Phoneme Recognition Using
Week 11-14:
Numerical
Projects in Biology/Chemistry/Physics/Engineering
-Week 11: Topic selection and background information
research
-Week 12-13: Project performance
-Week 14: Result visualizations, presentations, and
conclusions
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