A Sum of Gaussian Random Variables is a Gaussian Random Variable

A basic result from the theory of random variables is that when you sum two independent random variables, you convolve their probability density functions (PDF). (Equivalently, in the frequency domain, their characteristic functions multiply.)

That the sum of two independent Gaussian random variables is Gaussian follows immediately from the fact that Gaussians are closed under multiplication (or convolution).


Next Section:
The Bark Frequency Scale
Previous Section:
Gaussian Moments