Gaussian Window and Transform

The Gaussian window for FFT analysis was introduced in §3.11, and complex Gaussians (``chirplets'') were utilized in §9.10. 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 §9.4). The basic mathematics rederived here are well known (see, e.g., [192,5]), while the application to spectral modeling of sound remains a topic under development.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.