Gaussian Window and TransformThe Gaussian window for FFT analysis was introduced in §3.11, and complex Gaussians (``chirplets'') were utilized in §10.6. For reference in support of these topics, this appendix derives some additional properties of the Gaussian, defined by
and discusses some interesting applications in spectral modeling (the subject of §10.4). The basic mathematics rederived here are well known (see, e.g., [202,5]), while the application to spectral modeling of sound remains a topic under development.
Gaussians Closed under Multiplication