Gaussian Window and TransformFigure 3.36 shows an example length Gaussian window and its transform. The sigma parameter was set to so that simple truncation of the Gaussian yields a side-lobe level better than dB. Also overlaid on the window transform is a parabola; we see that the main lobe is well fit by the parabola until the side lobes begin. Since the transform of a Gaussian is a Gaussian (exactly), the side lobes are entirely caused by truncating the window.
Gaussian function can be found in Appendix D.
Exact Discrete Gaussian Window
Matlab for the Gaussian Window