**PHYSICS
SEMINAR**

**Randall
D. Peters**

Department of Physics

Mercer University

Wednesday,
January 14, 2004

Willet Science Center 101

"Sophisticated Spreadsheet
Digital Data Processing"

**
Abstract: **
The modern computer could not have developed without solid state electronics.
Similarly, many algorithms that have become essential to modern computing
would not be feasible without the fast Fourier transform, which 'makes
technology fly' [1,2].
The well-known-to-the-public 'computer enhanced images', as will no doubt
be generated using raw data from the latest Mars rover--rely on complex
algebraic FFT operations based in the convolution theorem.
Even the great 20th century invention of MRI relies on such calculations.
Although such operations have greatly impacted the 2-dimensional world of
imagery (including the compression schemes used to produce popular photographic jpeg's) similar powerful analysis of 1-dimensional time records are
lagging way behind.
This may exist, in part,
because of unwarranted attention to steady state calculations involving
poles and zeros (Laplace transform treatment).
Whereas the existing 1-D filter world of digital signal processing (DSP)
does routinely use windows (such as the Hanning) to provide apodization (to
reduce artifacts due to the Gibb's effect), surprisingly few have discovered the
powerful kernels of Green's function type that are based on the Gaussian
function. In
this presentation using Excel, the power of the spreadsheet will be illustrated,
first as a means to improve intuitive understanding of digital techniques.
Examples will include autocorrelation and various filters, including
'smoothed' derivatives obtained from the product of a Hermite polynomial
with a Gaussian.
Not only is the spreadsheet pedagogically useful, but its potential
importance for practical applications will also be demonstrated, as illustrated
in the attached figure.
Figures of similar type were generated during oscillator damping studies,
the results of which will be part of an engineering handbook [3].
[1]
Barry Cipra, "The FFT: Making Technology Fly", SIAM News, Vol. 26, No.
3, May 1993--online at http://www.siam.org/siamnews/mtc/mtc593.htm

[2]
R. Peters, "Graphical explanation for the speed of the Fast Fourier
Transform", online at http://arxiv.org/html/math.HO/0302212

[3]
"Damping"* *(chapter), *Handbook
of Vibration * *and** Shock*, ed. Clarence deSilva, to be published by CRC.

*Please
join us for light refreshments outside WSC 109 at 4:15.
*

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