### Gaussian Window and Transform

Figure 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.

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

**Next Section:**

Exact Discrete Gaussian Window

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Matlab for the Gaussian Window