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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.

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Exact Discrete Gaussian Window
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Matlab for the Gaussian Window