# Plotting noise in mathematica

• Mathematica
Does anyone know how to plot noise in mathematica? I want to plot a normal distribution which is white noise in the time domain. This is because I want a constant power spectral density but Gaussian spread of values. Anyway I can plot a list of normal distributed numbers but want to know how to plot them on a graph with white noise distribution.

shoehorn
For a white noise time series based on draws from the standard normal distribution, you might choose to do something like the following.

Code:
w = RandomReal[NormalDistribution[0,1], 500];
ListLinePlot[w]

Is this what you're after?

Not quite, that plot goes from 0 to 500. I want to inject a signal into the noise, and at the moment I'm having to stretch the signal to a width of 500 (or however many data points I choose).

shoehorn
The usual tactic one adopts to model a stochastic process containing a deterministic signal is to, well, model a stochastic process containing a deterministic signal. For instance, suppose that you have experimental data that looks like a sinusoidal signal blurred with white noise. You can model such a thing in Mathematica by defining the deterministic and stochastic parts of the signal separately and then adding them.

Code:
sample_length = 1000;
w = RandomReal[NormalDistribution[0, 1], sample_length];
s = Table[2*Cos[t/50] + 0.6 \[Pi], {t, 1, sample_length}];
ListLinePlot[w + s]

http://img697.imageshack.us/img697/3527/signals.png [Broken]

You can of course adapt this idea to whatever you're looking at simply by changing the number of steps in the stochastic process you're generating.

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