The Fourier Transform of a Gaussian Function
is given by

The second integrand is Even, so integration over a symmetrical range gives 0. The value of the first integral is given by Abramowitz and Stegun (1972, p. 302, equation 7.4.6)

so a Gaussian transforms to a Gaussian.

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, 1972.

© 1996-9

1999-05-26