# Noise Generator (Gaussian) (G Dataflow)

Version:

Generates a signal containing a Gaussian white noise wave.

## offset

DC offset of the signal.

Default: 0

## reset

A Boolean that controls the reseeding of the noise sample generator after the first execution of the node. By default, this node maintains the initial internal seed state.

 True Accepts a new seed and begins producing noise samples based on the seed. If the given seed is less than or equal to 0, the node ignores a reset value of True and resumes producing noise samples as a continuation of the previous sequence. False Resumes producing noise samples as a continuation of the previous noise sequence. The node ignores new seed inputs while reset is False.

Default: False

## standard deviation

Standard deviation of the noise you generate.

Default: 1

## seed

A number that initializes the noise generator.

If reset is unwired, this node maintains the internal seed state.

 seed is greater than 0 Generates noise samples based on the given seed value. For multiple calls to the node, the node accepts or rejects new seed inputs based on the given reset value. seed is less than or equal to 0 Generates a random seed value and produces noise samples based on that seed value. For multiple calls to the node, if seed remains less than or equal to 0, the node ignores the reset input and produces noise samples as a continuation of the initial noise sequence.

Default: -1

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## sample rate

Sample rate in samples per second.

This input is available only if you configure this node to return a waveform.

Default: 1000

## samples

Number of samples in the signal.

This input is available only if you configure this node to return a waveform or an array of double-precision, floating-point numbers.

Default: 1000

## t0

Timestamp of the output signal. If this input is unwired, this node uses the current time as the timestamp of the output signal.

This input is available only if you configure this node to return a waveform.

## Gaussian white noise

Gaussian-distributed, pseudorandom pattern.

This output can return the following data types:

• Waveform
• Double-precision, floating-point number
• 1D array of double-precision, floating-point numbers

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Generating the Gaussian White Noise

This node 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 node 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

$f\left(x\right)=\frac{1}{s\sqrt{2\pi }}{e}^{\left(\left(-\frac{1}{2}\right){\left(\frac{x}{s}\right)}^{2}\right)}$

where s is the absolute value of standard deviation. You can compute the expected values, $E\left\{\cdot \right\}$, using the following formula:

$E\left(x\right)={\int }_{-\infty }^{\infty }x\left(f\left(x\right)\right)dx$

The following equations define the expected mean value $\mu$ and the expected standard deviation value $\sigma$ of the pseudorandom sequence:

$\mu =E\left\{x\right\}=0$
$\sigma ={\left[E\left\{{\left(x-\mu \right)}^{2}\right\}\right]}^{1/2}=s$

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 $\sigma$.

## Application of the Gaussian White Noise

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.

Where This Node Can Run:

Desktop OS: Windows

FPGA: DAQExpress does not support FPGA devices