References (Gabor 1946, Heisenberg 1927)

Here are some references you might want to read in order to learn more about the sense in which the Gaussian filter is optimal.
  author    = "D. Gabor",
  title     = "Theory of Communication",
  journal   = "J. Inst. Elec. Eng.",
  volume    = "Vol.93",
  number    = "Part III",
  year      = 1946,
  pages     = "429--457"           }

 author={W. Heisenberg},
 journal="Z. Physik",

Alternatively, you can look at the timebandwidth.m script, as well as extents.m, etc..

You might also find a 1991 paper on chirplets

  author = "Mann, Steve and Haykin, Simon",
  title = "The Chirplet Transform: A Generalization of
            {G}abor's Logon Transform",
  journal = "Vision Interface '91",
  publisher = "",
  organization = "Canadian Image Processing and Patern Recognition Society",
  address = "Calgary, Alberta",
  month = "June 3-7",
  pages = "205--212",
  note = "ISSN 0843-803X",
  year = "1991"
would make an interesting read, because it begins with a review of some of the materials in the above two references.