Gaussian Window and Transform

Figure 3.36 shows an example length $M=21$ Gaussian window and its transform. The sigma parameter was set to $M/8$ so that simple truncation of the Gaussian yields a side-lobe level better than $-80$ 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.

Figure 3.36: Gaussian window and transform.

More properties and applications of the Gaussian function can be found in Appendix D.