Re: Multidimensional Fourier Transform
- To: mathgroup at christensen.cybernetics.net
- Subject: [mg310] Re: [mg300] Multidimensional Fourier Transform
- From: Brian Evans <ble at forney.eecs.berkeley.edu>
- Date: Fri, 9 Dec 1994 13:36:45 -0800
I wrote a m-D Fourier transform package that is embedded in a
larger set of signal processing packages. A version of the
packages is available from MathSource as item 0202-240. I'll
append the MathSource automatic response at the end. The
MathSource FTP site is mathsource.wri.com.
As a student at Georgia Tech, Joe Winograd enhanced the m-D
Fourier transform package to support non-separable transforms
in the context of comparing computed tomography algorithms using
exact-precision arithmetic against those using floating-point
arithmetic. He wrote a Mathematica notebook on his work which
has been accepted as a journal paper. Feel free to contact Joe
who is now a graduate student at Boston University and who
can be reached by e-mail at winograd at buengc.bu.edu.
I graduated from Georgia Tech in September, 1993, and I am now
a post-doctoral researcher at U.C. Berkeley.
Two commerical versions of the signal processing packages will
be going into production in January.
Brian
P.S. I sent e-mail to mathsource at wri.com, and the automatic server
matched 19 items for the search phrase "find signal processing",
but I'm only going to list the signal processing packages entry:
>> find signal processing
19 items matched your request.
0202-240: Signal Processing Packages and Notebooks Version 2.9.5 (March 9,
1994)
Authors: Brian Evans, James McClellan, Kevin West, Wallace
McClure, Lena Karam, and Jim Proctor
A hierarchical set of packages to perform basic analyses of
signals (functions) and systems (operators). The packages are
based on transform theory and implement many concepts from linear
systems theory. They support (bilateral) z- and Laplace
transforms, as well as continuous-time, discrete-time, and
discrete Fourier transforms, all in arbitrary dimension. These
rule bases can fully justify their answers (i.e, show the
intermediate steps) and allow users to specify their own transform
pairs.
The packages can perform a variety of operations for symbolic,
graphical and numerical operations of signals and systems.
Symbolic analyses include simplification of expressions,
determination of data types, and reasoning about properties of
signals, such as stability. For 1-D and 2-D signals, plotting
capabilities include discrete time-domain plots, magnitude and
phase responses, and pole-zero diagrams, including the region of
convergence, for z- and Laplace transforms. Root loci can also be
plotted for one varying parameter.
Accompanying the packages are tutorial notebooks on analog filter
design, discrete Fourier analysis, convolution, and the
z-transform. Other notebooks provide on-line help.
0011: README.txt Installation notes (March 1994; 24 kilobytes)
0022: CHANGES.txt Text file documentation changes (March 1994; 53
kilobytes)
0033: CHANGES-SUMMARY.txt Text file summarizing changes (March
1994; 14 kilobytes)
0044: usage.ps PostScript version of the reference guide (March
1994; 247 kilobytes)
0055: usage.tex TeX version of the reference guide (March 1994;
138 kilobytes)
0066: usersguide.ps PostScript version of the users' guide (March
1994; 343 kilobytes)
0077: usersguide.tex TeX version of the users' guide (March 1994;
95 kilobytes)
0088: SigProc2.0.mac.sea.hqx Macintosh Binhexed self-extracting
archive (March 1994; 1906 kilobytes)
0099: SigProc2.0.tar.Z Unix Compressed, tar file (March 1994;
1669 kilobytes)
0101: SigProc2-IBM-PC.zip PK-Zip archive (March 1994; 1001
kilobytes)