The plot thickens - Solution

The probability density function of the normal or Gaussian distribution, is:

y(t)=(1/(sigma*(2*pi)^0.5))*e^(-0.5*((t-mu)/sigma)^2)

where mu is the mean and sigma the standard deviation.

y(t) and amplitude spectrum with mu=0 sigma=0.05

Normal distribution y(t)=(1/(sigma*(2*pi)^0.5))*e^(-0.5*((t-mu)/sigma)^2) with sigma = 0.05 and mu 0

Frequency spectrum of normal distribution function y(t)=(1/(sigma*(2*pi)^0.5))*e^(-0.5*((t-mu)/sigma)^2) with sigma = 0.05 and mu 0

y(t) and amplitude spectrum with mu=0 sigma=0.1

Normal distribution y(t)=(1/(sigma*(2*pi)^0.5))*e^(-0.5*((t-mu)/sigma)^2) with sigma = 0.1 and mu 0

Frequency spectrum of Normal distribution y(t)=(1/(sigma*(2*pi)^0.5))*e^(-0.5*((t-mu)/sigma)^2) with sigma = 0.1 and mu 0

y(t) and amplitude spectrum with mu=0 sigma=0.5

Normal distribution y(t)=(1/(sigma*(2*pi)^0.5))*e^(-0.5*((t-mu)/sigma)^2) with sigma = 0.5 and mu 0

Frequency spectrum of Normal distribution y(t)=(1/(sigma*(2*pi)^0.5))*e^(-0.5*((t-mu)/sigma)^2) with sigma = 0.5 and mu 0

Notice that the spread of frequencies has narrowed as as the spread of the original function has increased.

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