# Documentation

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# Random Source

Generate randomly distributed values

## Library

Sources

`dspsrcs4`

## Description

The Random Source block generates a frame of M values drawn from a uniform or Gaussian pseudorandom distribution, where you specify M in the Samples per frame parameter.

This reference page contains a detailed discussion of the following Random Source block topics:

### Distribution Type

When the Source type parameter is set to `Uniform`, the output samples are drawn from a uniform distribution whose minimum and maximum values are specified by the Minimum and Maximum parameters, respectively. All values in this range are equally likely to be selected. A length-N vector specified for one or both of these parameters generates an N-channel output (M-by-N matrix) containing a unique random distribution in each channel.

For example, specify

• Minimum = `[ 0 0 -3 -3]`

• Maximum = ```[10 10 20 20]```

to generate a four-channel output whose first and second columns contain random values in the range [0, 10], and whose third and fourth columns contain random values in the range [-3, 20]. When you specify only one of the Minimum and Maximum parameters as a vector, the block scalar expands the other parameter so it is the same length as the vector.

When the Source type parameter is set to `Gaussian`, you must also set the Method parameter, which determines the method by which the block computes the output, and has the following settings:

• `Ziggurat` — Produces Gaussian random values by using the Ziggurat method.

• `Sum of uniform values` — Produces Gaussian random values by adding and scaling uniformly distributed random signals based on the central limit theorem. This theorem states that the probability distribution of the sum of a sufficiently high number of random variables approaches the Gaussian distribution. You must set the Number of uniform values to sum parameter, which determines the number of uniformly distributed random numbers to sum to produce a single Gaussian random value.

For both settings of the Method parameter, the output samples are drawn from the normal distribution defined by the Mean and Variance parameters. A length-N vector specified for one or both of the Mean and Variance parameters generates an N-channel output (M-by-N frame matrix) containing a distinct random distribution in each column. When you specify only one of these parameters as a vector, the block scalar expands the other parameter so it is the same length as the vector.

### Output Complexity

The block's output can be either real or complex, as determined by the `Real` and `Complex` options in the Complexity parameter. These settings control all channels of the output, so real and complex data cannot be combined in the same output. For complex output with a `Uniform` distribution, the real and imaginary components in each channel are both drawn from the same uniform random distribution, defined by the Minimum and Maximum parameters for that channel.

For complex output with a `Gaussian` distribution, the real and imaginary components in each channel are drawn from normal distributions with different means. In this case, the Mean parameter for each channel should specify a complex value; the real component of the Mean parameter specifies the mean of the real components in the channel, while the imaginary component specifies the mean of the imaginary components in the channel. When either the real or imaginary component is omitted from the Mean parameter, a default value of 0 is used for the mean of that component.

For example, a Mean parameter setting of ```[5+2i 0.5 3i]``` generates a three-channel output with the following means.

 Channel 1 mean real = 5 imaginary = 2 Channel 2 mean real = 0.5 imaginary = 0 Channel 3 mean real = 0 imaginary = 3

For complex output, the Variance parameter, σ2, specifies the total variance for each output channel. This is the sum of the variances of the real and imaginary components in that channel.

`${\sigma }^{2}={\sigma }_{\mathrm{Re}}^{2}+{\sigma }_{\mathrm{Im}}^{2}$`

The specified variance is equally divided between the real and imaginary components, so that

`$\begin{array}{c}{\sigma }_{\mathrm{Re}}^{2}=\frac{{\sigma }^{2}}{2}\\ {\sigma }_{\mathrm{Im}}^{2}=\frac{{\sigma }^{2}}{2}\end{array}$`

### Output Repeatability

The Repeatability parameter determines whether or not the block outputs the same signal each time you run the simulation. You can set the parameter to one of the following options:

• `Repeatable` — Outputs the same signal each time you run the simulation. The first time you run the simulation, the block randomly selects an initial seed. The block reuses these same initial seeds every time you rerun the simulation.

• `Specify seed` — Outputs the same signal each time you run the simulation. Every time you run the simulation, the block uses the initial seed(s) specified in the Initial seed parameter. Also see Specifying the Initial Seed.

• `Not repeatable` — Does not output the same signal each time you run the simulation. Every time you run the simulation, the block randomly selects an initial seed.

### Specifying the Initial Seed

When you set the Repeatability parameter to `Specify seed`, you must set the Initial seed parameter. The Initial seed parameter specifies the initial seed for the pseudorandom number generator. The generator produces an identical sequence of pseudorandom numbers each time it is executed with a particular initial seed.

### Specifying Initial Seeds for Real Outputs

To specify the N initial seeds for an N-channel real-valued output, Complexity parameter set to `Real`, provide one of the following in the Initial seed parameter:

• Length-N vector of initial seeds — Uses each vector element as an initial seed for the corresponding channel in the N-channel output.

• Single scalar — Uses the scalar to generate N random values, which it uses as the seeds for the N-channel output.

### Specifying Initial Seeds for Complex Outputs

To specify the initial seeds for an N-channel complex-valued output, Complexity parameter set to `Complex`, provide one of the following in the Initial seed parameter:

• Length-N vector of initial seeds — Uses each vector element as an initial seed for generating N channels of real random values. The block uses pairs of adjacent values in each of these channels as the real and imaginary components of the final output, as illustrated in the following figure.

• Single scalar — Uses the scalar to generate N random values, which it uses as the seeds for generating N channels of real random values. The block uses pairs of adjacent values in each of these channels as the real and imaginary components of the final output, as illustrated in the following figure.

### Sample Period

The Sample time parameter value, Ts, specifies the random sequence sample period when the Sample mode parameter is set to `Discrete`. In this mode, the block generates the number of samples specified by the Samples per frame parameter value, M, and outputs this frame with a period of M*Ts.

When Sample mode is set to `Continuous`, the block is configured for continuous-time operation, and the Sample time and Samples per frame parameters are disabled. Note that many DSP System Toolbox™ blocks do not accept continuous-time inputs.

## Parameters

Source type

The distribution from which to draw the random values, `Uniform` or `Gaussian`. For more information, see Distribution Type.

Method

The method by which the block computes the Gaussian random values, `Ziggurat` or ```Sum of uniform values```. This parameter is enabled when Source type is set to `Gaussian`. For more information, see Distribution Type.

Minimum

The minimum value in the uniform distribution. This parameter is enabled when you select `Uniform` from the Source type parameter. Tunable in Simulation mode only.

Maximum

The maximum value in the uniform distribution. This parameter is enabled when you select you select `Uniform` from the Source type parameter. Tunable in Simulation mode only.

Number of uniform values to sum

The number of uniformly distributed random values to sum to compute a single number in a Gaussian random distribution. This parameter is enabled when the Source type parameter is set to `Gaussian`, and the Method parameter is set to `Sum of uniform values`. For more information, see Distribution Type.

Mean

The mean of the Gaussian (normal) distribution. This parameter is enabled when you select `Gaussian` from the Source type parameter. Tunable in Simulation mode only.

Variance

The variance of the Gaussian (normal) distribution. This parameter is enabled when you select `Gaussian` from the Source type parameter. Tunable in Simulation mode only.

Repeatability

The repeatability of the block output: `Not repeatable`, `Repeatable`, or `Specify seed`. In the `Repeatable` and ```Specify seed``` settings, the block outputs the same signal every time you run the simulation. For details, see Output Repeatability.

Initial seed

The initial seed(s) to use for the random number generator when you set the Repeatability parameter to ```Specify seed```. For details, see Specifying the Initial Seed. Tunable in Simulation mode only.

Inherit output port attributes

When you select this check box, block inherits the sample mode, sample time, output data type, complexity, and signal dimensions of the signal from the downstream block. When you select this check box, the Sample mode, Sample time, Samples per frame, Output data type, and Complexity parameters are disabled.

Suppose you want to back propagate a 1-D vector. The output of the Random Source block is a 1-D vector of length M, where length M is inherited from the downstream block. When the Minimum, Maximum, Mean, or Variance parameter specifies N channels, the 1-D vector output contains M/N samples from each channel. An error occurs in this case when M is not an integer multiple of N.

Suppose you want to back propagate a M-by-N signal. When N>1, your signal has N channels. When N = 1, your signal has M channels. The value of the Minimum, Maximum, Mean, or Variance parameter can be a scalar or a vector of length equal to the number of channels. You can specify these parameters as either row or column vectors, except when the signal is a row vector. In this case, the Minimum, Maximum, Mean, or Variance parameter must also be specified as a row vector.

Sample mode

The sample mode, `Continuous` or `Discrete`. This parameter is enabled when the Inherit output port attributes check box is cleared.

Sample time

The sample period, Ts, of the random output sequence. The output frame period is M*Ts. This parameter is enabled when the Inherit output port attributes check box is cleared.

Samples per frame

The number of samples, M, in each output frame.

This parameter is enabled when the Inherit output port attributes check box is cleared.

Output data type

The data type of the output, single-precision or double-precision. This parameter is enabled when the Inherit output port attributes check box is cleared.

Complexity

The complexity of the output, `Real` or `Complex`. This parameter is enabled when the Inherit output port attributes check box is cleared.

## Supported Data Types

• Double-precision floating-point

• Single-precision floating-point

 Discrete Impulse DSP System Toolbox Maximum DSP System Toolbox Minimum DSP System Toolbox Signal From Workspace DSP System Toolbox Standard Deviation DSP System Toolbox Variance DSP System Toolbox Constant Simulink Random Number Simulink Signal Generator Simulink `rand` MATLAB `randn` MATLAB `RandStream` MATLAB