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Gaussian Function Properties
Subsections
Gaussian Window and Transform
Gaussians are Closed under Multiplication
Product of Two Gaussian PDFs
Gaussians are Closed under Convolution
Infinite Flatness at Infinity
Integral of a Complex Gaussian
Area Under a Real Gaussian
Gaussian Integral with Complex Offset
Fourier Transform of Complex Gaussian
Alternate Proof
Why Gaussian?
Central Limit Theorem
Iterated Convolutions
Binomial Distribution
Boltzman Energy Distribution for a Potential Well
Gaussian Probability Density Function
Maximum Entropy Property
Entropy of a Probability Distribution
Example: Random Bit String
Maximum Entropy Distributions
Uniform Distribution
Exponential Distribution
Gaussian Distribution
Gaussian Moments
Gaussian Mean
Gaussian Variance
Higher Order Moments Revisited
Moment Theorem
Gaussian Characteristic Function
Gaussian Central Moments
Sums of Gaussian Random Variables
Uncertainty Principle
History of the Gaussian Function
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[How to cite this work]
[Order a printed hardcopy]
``
Spectral Audio Signal Processing
'', by
Julius O. Smith III
, (August 2008 Draft).
Copyright ©
2008-08-13
by
Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),
Stanford University
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