Gaussian Window and Transform

The Gaussian ``bell curve'' is possibly the only smooth, nonzero function, known in closed form, that transforms to itself.^4.10

It also achieves the minimum time-bandwidth product

when ``width'' is defined as the square root of its second central moment. For even functions ,

Since the true Gaussian function has infinite duration, in practice we must window it with some usual finite window, or truncate it.

Depalle [57] suggests using a triangular window raised to some power for this purpose, which preserves the absence of sidelobes for sufficiently large . It also preserves non-negativity of the transform.

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Subsections

• Matlab for the Gaussian Window
• Gaussian Window and Transform
• Exact Discrete Gaussian Window

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Next: Matlab for the Gaussian Window

Order a Hardcopy of Spectral Audio Signal Processing

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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.