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Re: Multidimensional Fourier Transform

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  • Subject: [mg310] Re: [mg300] Multidimensional Fourier Transform
  • From: Brian Evans <ble at>
  • 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

	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

	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.


P.S.  I sent e-mail to mathsource at, 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,
          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

          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

          0033:  CHANGES-SUMMARY.txt Text file summarizing changes (March
                 1994; 14 kilobytes)

          0044: PostScript version of the reference guide (March
                 1994; 247 kilobytes)

          0055:  usage.tex TeX version of the reference guide (March 1994;
                 138 kilobytes)

          0066: 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: PK-Zip archive (March 1994; 1001

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