Plotting White Noise Distribution in Mathematica

[madness]

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.

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

Is this what you're after?

 

[madness]

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.

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

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.

 

[madness]

With this method you define 1000 random numbers and insert them at unit intervals for the noise. Does this mean the noise is white noise since the numbers are uncorrellated at each point in time? Or does the fact that the noise is there at every sample point count as a correlation?