I s'pose i can edit this later and add some C-like pseudo-code to show this explicitly. You can vary the output settings of the Signal Generator block while a simulation is in progress. (so the 'power spectral density" or power per unit frequency is 1/Nyquist.) scale it and offset it however you please. You can generate a phase-shifted wave at other than 180 degrees in a variety of ways, including connecting a Clock block signal to a MATLAB Fcn block and writing the equation for the particular wave. the virtually-gaussian and "white" signal generated as described has a finite power (which is the variance and is 1) and finite bandwidth which, expressed as one-sided, is Nyquist. a "power signal" with flat spectrum all the way to infinity also has infinite power. "white noise" is, of course a misnomer, even for analog signals. pseudo-random numbers are "good" (that is they exhibit independence from each other), this sum will be as "white" as you can get a discrete-time signal to be. pseudo-random number $x$ (say using rand() or frand(), if it's a good version) that ranges from 0 to 1 (that is $0 \le x < 1$), then if you do that 12 times, add up all 12 of the supposedly independent and uncorrelated values, and subtract 6.0 from that sum, you will have something that is very close to a unit-variance and zero-mean gaussian random number. I realize this question popped up in current view because modified his/her 2013 answer.
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