Gaussian White Noise VI

	initialize? controls the reseeding of the noise sample generator after the first call of the VI. If initialize? is TRUE, accepts a new state or new seed value and begins producing noise samples based on the new state or new seed value. If initialize? is FALSE, this VI maintains the initial internal seed state and resumes producing noise samples as a continuation of the previous noise sequence. The default is TRUE.
	samples is the number of samples of the Gaussian noise pattern. samples must be greater than 0. The default is 128.
	standard deviation is the standard deviation of the Gaussian probability density function. The default is 1.0.
	seed determines how to generate the internal seed state when initialize? is TRUE. If seed is greater than 0, this VI uses seed to generate the internal state directly. If seed is less than or equal to 0, this VI uses a random number to generate the internal state. seed must not be a multiple of 16384. If initialize? is FALSE, this VI ignores seed. The default is -1.
	Gaussian noise pattern returns the Gaussian-distributed, pseudorandom pattern.
	error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Gaussian White Noise Details

The Gaussian White Noise VI generates the Gaussian-distributed pseudorandom sequence using a modified version of the Box-Muller method to transform uniformly distributed random numbers into Gaussian-distributed random numbers. This VI generates the uniform pseudorandom numbers using the Wichmann-Hill generator.

Given that the probability density function, f(x), of the Gaussian-distributed Gaussian noise pattern is

where s is the absolute value of the specified standard deviation. You can compute the expected values, E{·}, using the following formula:

The following equations define the expected mean value, µ, and the expected standard deviation value, , of the pseudorandom sequence:

µ = E{x} = 0

= [E{x – µ}²]^1/2 = s

The pseudorandom sequence produces approximately 6.95 * 10¹² samples before the pattern repeats itself. The probability density function (PDF) of the pseudorandom sequence approximates a Gaussian PDF with peak values of at least 6.

Gaussian white noise provides a realistic simulation of some real-world situations. Because of its independent statistical characteristics, Gaussian white noise also often acts as the source of other random number generators. The additive white Gaussian noise (AWGN) channel model is widely used in communications.

You can use the initialize? input to generate a long random noise sequence block by block. The following block diagram shows two ways to generate identical 300-sample Gaussian white noise sequences with a seed of 2.

You also can use the Gaussian White Noise Waveform VI to generate a Gaussian white noise signal.