The Mathematica documentation center provides an example of how to add noise to a process: White Noise Process.
\[ScriptCapitalP] = TransformedProcess[
Cos[t/8] + noise[t],
noise \[Distributed] WhiteNoiseProcess[UniformDistribution[{-1/5, 1/5}]],
t];
data = RandomFunction[\[ScriptCapitalP], {0, 200}];
ListPlot[data, Filling -> Axis]
I'm also able to do the same with Gaussian noise, in which case I use NormalDistribution[0, 1]
instead of UniformDistribution[{-1/5, 1/5}]
.
I have now two problems:
- The first one is that I want the standard derivation to be a function of time, so
NormalDistribution[0, f[t]]
, but this doesn't work. - The second problem is that I always get nothing when I choose the variance to be zero, which should effectively correspond to no noise.
Can someone help?
PDF[NormalDistribution[0, 0], x]
, which throws the errorNormalDistribution::posprm: "Parameter 0 at position 2 in NormalDistribution[0,0] is expected to be positive."
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