Random Source

Generate randomly distributed values

• 

Libraries:
DSP System Toolbox / Sources

Description

The Random Source block outputs a random signal with a uniform or Gaussian (normal) pseudorandom distribution. The block uses the Mersenne Twister random number generator to generate the sequence. The settings in the block dialog box determine the size, data type, and complexity of the signal.

The block can generate a single-channel or a multichannel signal.

Examples

Generate Random Signal with Uniform Distribution

Open the GenerateUniformSignal.slx model. The Random Source block in the model has the Distribution parameter set to Uniform. The minimum and maximum values of the uniform distribution are 1 and 3, respectively.

Set the Samples per frame parameter to 512. The output random signal contains 512 samples in each channel (frame). Set the Sample time parameter to 0.1. Setting the Signal complexity to Real generates a real signal. Since the Initial seed parameter in the block dialog box is set to 1, the random signal that the block outputs is repeatable; that is, each time you simulate the model, the block generates the same pseudorandom sequence.

Run the model. The Random Source block generates a real single-channel signal with a uniform distribution. View the signal in the time scope.

The frame rate of the block MTs is . View the frame rate in the timing legend.

Change the Sample time to 0.2 seconds and rerun the model. The output frame rate of the block is now .

Generate Random Signal with Gaussian Distribution

Open the GenerateGaussianSignal.slx model. The Random Source block in the model has the Distribution parameter set to Gaussian.

Generate Single-Channel Signal

Set the Mean and Variance parameters to 0 and 0.5, respectively. Because these values are scalars, the block generates a single-channel random signal. With the Samples per frame parameter set to 512, the block generates a 512-by-1 signal.

Generate Multichannel Signal

Set the Mean or Variance parameter to a row vector of four elements to generate a random signal with four channels. The value of the Mean parameter in this model is [0 2 4 6]. The Variance parameter must be a scalar or a row vector of four elements to match the dimensions of the Mean parameter. The value of the Variance parameter in this model is 0.5.

Run the model. The block generates a multichannel Gaussian random signal of size 512-by-4.

Repeat Random Signal Output

Use the Repeatability parameter to repeat the block output.

Open the RepeatRandomSignal.slx model. Set Repeatability to 'Specify Seed' to produce the same pseudorandom sequence each time you simulate the model. Specify the random seed as 123 through the Initial seed parameter.

Run the model.

Repeat the simulation and notice that the output values are exactly the same as the previous run.

    2.3929    2.9615    1.8771
    1.5723    2.3697    1.1194
    1.4537    1.9619    1.7961
    2.1026    1.7842    2.4760
    2.4389    1.6864    1.3650
    1.8462    2.4581    1.3509

Change the seed to 456 and run the model. The output values change but are exactly the same in subsequent simulations.

    1.4975    2.7714    2.1514
    1.3261    2.5182    1.2922
    2.5673    1.3622    2.3732
    2.6170    1.3003    1.9376
    2.2513    1.8714    2.1400
    2.2082    1.7705    2.2914

Set Repeatability to 'Not repeatable' and run the model.

    1.1354    2.6698    2.1185
    2.0068    1.3143    1.6524
    2.4179    1.6153    1.5030
    2.4327    1.9889    1.1016
    2.6093    1.8927    1.4261
    1.2325    1.0864    2.2237

Repeat the simulation. The output signal is now different compared to the previous run.

    1.1801    1.0135    2.6225
    1.4634    1.8974    1.1402
    2.9918    1.0033    1.6790
    1.1409    2.4337    1.9416
    1.0579    2.7062    2.4268
    2.2496    1.5049    2.0864

Generate Complex Random Signal

Generate a complex random signal by setting the Signal complexity parameter to Complex.

Open the ComplexRandomSignal model. The Distribution parameter in the Random Source block is set to Uniform. The minimum and maximum values of the uniform distribution are 1 and 3, respectively.

Run the model. The block generates a complex scalar random signal with a uniform distribution. The Complex to Real-Imag block splits the signal into real and imaginary components. Plot the data using the XY Graph block.

Change the distribution to Gaussian. Set the Mean parameter to a complex number. 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. If you omit the real or imaginary component from the Mean parameter, the block uses a default value of 0 as the mean of that component.

The variance must always be real and positive.

Inherit Signal Properties Via Output Port

Select the Inherit via output port parameter to inherit the properties of the random signal through back propagation.

Open the InheritSignalProperties model. The model adds the outputs of the Random Source block and the Sine Wave block, and plots the resulting noisy sinusoidal signal in the time scope.

The Random Source block generates a random signal with a Gaussian distribution. The mean and variance of the distribution is 0 and 0.01, respectively.

Select the Inherit via output port parameter in the Random Source block. The block inherits the signal properties such as the size, data type, complexity, and sample time from the Sine Wave block via back propagation. The Sine Wave block generates a complex sinusoidal signal with a sample time of 0.001 seconds. The Random Source block inherits these properties and generates a random signal with the same properties.

Run the model. View the real and imaginary components of the noisy sinusoidal signal in the time scope.

Estimate Frequency-Domain Transfer Function of System Using Random Excitation Input

This example shows how to use the Discrete Transfer Function Estimator block to estimate the frequency-domain transfer function of a system.

Open the ex_discretetransferfunctionestimator.slx model. The Random Source block generates the system input signal that you pass through the x port of the Discrete Transfer Function Estimator block. The sample rate of the input signal is 44.1 KHz. This input signal passes through a lowpass filter with a normalized cutoff frequency of 0.3. The filtered signal represents the system output signal that you input through the port y of the Discrete Transfer Function Estimator block. Because the Discrete Transfer Function Estimator block outputs complex values, compute the magnitude of the output signal to generate a plot of the transfer function estimate.

Run the model. The array plot shows the system transfer function, a lowpass filter that matches the frequency response of the Discrete FIR Filter block.

Extended Examples

Compute Moving Variance of Noisy Square Wave Signal

Compare the sliding window variance method and the exponentially weighted variance method in Simulink^® using the Moving Variance block.

• Open Model

Analyze a Subband of Input Frequencies Using Zoom FFT

Compute the zoom FFT of a sine wave in Simulink.

• Open Model

Adapt Multiple Filters Using LMS Update Block

Adapt multiple filters independently using the same LMS Update block. Use the Adapt port of the LMS Update block to selectively enable or disable the filters from being adapted.

• Open Model

Estimate Data Series Using Forward Linear Predictor

Use the Autocorrelation LPC block to estimate the future values of signal.

• Open Model

Ports

Output

Port_1 — Signal of randomly distributed values

scalar | vector | matrix

Signal of random values with uniform or Gaussian (normal) distribution. The settings in the block dialog box determine the size, data type, and complexity of the signal.

The block can generate a single-channel or a multichannel signal. The Samples per frame parameter determines the number of samples in each channel (column) of the signal. The Output data type and Signal complexity parameters determine the data type and complexity of the signal.

Data Types: single | double
Complex Number Support: Yes

Parameters

Distribution Settings

Distribution — Uniform or Gaussian

Uniform (default) | Gaussian

Specify the distribution from which to draw the random values as one of these:

• Uniform –– The block draws the output samples from a uniform distribution. You can specify the minimum and maximum values of the distribution using the Minimum and Maximum parameters, respectively. You can generate a complex number from the uniform distribution by setting the Signal complexity parameter to Complex.

  All values in this [Minimum Maximum] range have an equal likelihood to be selected.

  For an example, see Generate Random Signal with Uniform Distribution.

• Gaussian –– The block produces Gaussian random values by using the Ziggurat method. You can specify the mean and variance of the distribution using the Mean and Variance parameters. You can generate a complex Gaussian signal by setting the Signal complexity parameter to Complex.

  For an example, see Generate Random Signal with Gaussian Distribution.

Minimum — Minimum value of uniform distribution

0 (default) | scalar | row vector

Specify the minimum value in the uniform distribution as a scalar or a row vector of length N. When you specify a row vector, the block generates an M-by-N matrix containing a unique random distribution in each channel. M is the value you specify in the Samples per frame parameter.

For example, when you set Minimum to [0 0 -3 -3] and Maximum to [10 10 20 20], the block generates 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].

The Minimum and Maximum values must be scalars or have the same number of columns. When you specify only one of the Minimum and Maximum parameters as a vector, the block expands the other parameter so that it is the same length as the vector.

Tunable: Yes

Dependencies

To enable this parameter, set Distribution to Uniform.

Maximum — Maximum value of uniform distribution

1 (default) | scalar | row vector

Specify the maximum value in the uniform distribution as a scalar or a row vector of length N. When you specify a row vector, the block generates an M-by-N matrix containing a unique random distribution in each channel. M is the value you specify in the Samples per frame parameter.

For example, when you set Minimum to [0 0 -3 -3] and Maximum to [10 10 20 20], the block generates 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].

The Minimum and Maximum values must be scalars or have the same number of columns. When you specify only one of the Minimum and Maximum parameters as a vector, the block expands the other parameter so it is the same length as the vector.

Tunable: Yes

Dependencies

To enable this parameter, set Distribution to Uniform.

Mean — Mean value of Gaussian distribution

0 (default) | scalar | row vector

Specify the mean of the Gaussian (normal) distribution as a scalar or a row vector of length N. When you specify a row vector, the block generates an M-by-N matrix containing a distinct random distribution in each channel. M is the value you specify in the Samples per frame parameter.

The Mean and Variance values must be scalars or have the same number of columns. When you specify only one of the Mean and Variance parameters as a vector, the block expands the other parameter so that it is the same length as the vector.

To generate a complex output signal with a Gaussian distribution, set Signal complexity to Complex and specify a complex value in the Mean parameter. For more information, see the Signal complexity parameter description.

Tunable: Yes

Dependencies

To enable this parameter, set Distribution to Gaussian.

Complex Number Support: Yes

Variance — Variance of Gaussian distribution

1 (default) | scalar | row vector

Specify the variance of the Gaussian (normal) distribution as a scalar or a row vector of length N. When you specify a row vector, the block generates an M-by-N matrix containing a distinct random distribution in each channel. M is the value you specify in the Samples per frame parameter.

The Mean and Variance values must be scalars or have the same number of columns. When you specify only one of the Mean and Variance parameters as a vector, the block expands the other parameter so that it is the same length as the vector.

To generate a complex output signal with a Gaussian distribution, the Variance parameter σ² specifies the total variance for each output channel. This value is the sum of the variances of the real and imaginary components in that channel. For more information, see the Signal complexity parameter description.

Dependencies

To enable this parameter, set Distribution to Gaussian.

Random Generator Settings

Repeatability — Option to repeat block output

Specify seed (default) | Not repeatable

Option to repeat block output, specified as one of these:

• Specify seed — The block uses the initial seed that you specify in the Initial seed parameter to produce a repeatable output for every simulation.

• Not repeatable — The block randomly selects an initial seed and produces a different pseudorandom sequence for every simulation.

For an example that shows the behavior of this parameter, see Repeat Random Signal Output.

Initial seed — Initial seed for random number generator

1 (default) | scalar

Specify the initial seed(s) for the random number generator as a scalar. The generator produces an identical sequence of pseudorandom numbers each time you simulate the block with a particular initial seed.

Dependencies

To enable this parameter, set Repeatability to Specify seed.

Signal Properties

Inherit via output port — Inherit output port parameters from downstream block

off (default) | on

When you select this check box, the block inherits the signal properties such as the samples per frame, output data type, signal complexity, and sample time from the downstream block and disables the corresponding parameters in the block dialog box. For an example, see Inherit Signal Properties Via Output Port.

Suppose that 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 the block inherits the length M 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 that 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 row or column vectors, except when the signal is a row vector. In this case, you must specify the Minimum, Maximum, Mean, or Variance parameter as a row vector.

Sample time — Output sample period

1 (default) | −1 | real positive scalar

Specify the sample period T_s of the random output sequence as a real positive scalar or -1. The output frame period is MT_s.

If T_s = −1, the block inherits the output sample period from its output port, but determines the dimensions and complexity of the signal from the block settings.

Dependencies

To enable this parameter, clear the Inherit via output port parameter.

Samples per frame — Samples per output frame

1 (default) | positive integer

Specify the number of samples M in each output frame as a positive integer. The output frame period is MT_s, where T_s is the value you specify in the Sample time parameter.

Dependencies

To enable this parameter, clear the Inherit via output port parameter.

Signal complexity — Complexity of output

Real (default) | Complex

Specify the complexity of the output as Real or Complex. These settings control all channels of the output. The real and complex components of the output are statistically independent.

For a complex output with a Uniform distribution, the block draws the real and imaginary components in each channel from the same uniform random distribution, defined by the Minimum and Maximum parameters for that channel.

For a complex output with a Gaussian distribution, the block draws the real and imaginary components in each channel from normal distributions with different means. In this case, the Mean parameter for each channel must be 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 you omit the real or imaginary component from the Mean parameter, the block uses a default value of 0 for the mean of that component.

For example, a Mean parameter setting of [5+2i 0.5 3i] generates a three-channel output with these mean values.

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

For a more detailed example, see Generate Complex Random Signal.

For a complex output, the Variance parameter σ² specifies the total variance for each output channel. This value 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 block divides the variance value you specify equally between the real and imaginary components.

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

Dependencies

To enable this parameter, clear the Inherit via output port parameter.

Output data type — Output data type

double (default) | single

Specify the data type of the output as double precision or single precision.

Dependencies

To enable this parameter, clear the Inherit via output port parameter.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

Specify the type of simulation to run. You can set this parameter to:

• Interpreted execution –– Simulate model using the MATLAB^® interpreter. This option shortens startup time.

• Code generation –– Simulate model using generated C code. The first time you run a simulation, Simulink generates C code for the block. The C code is reused for subsequent simulations as long as the model does not change. This option requires additional startup time but provides faster subsequent simulations.

Block Characteristics

Data Types	double | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

More About

Uniform Distribution

Uniform distribution is a type of probability distribution in which all outcomes are equally likely.

Scalar Random Variable

Consider a scalar random variable X that the block draws from a uniform distribution U:

X ~ U([A,B]), where A and B are the minimum and maximum values of the distribution, respectively.

Alternatively, you can write X in terms of a scaled normalized uniform variable:

$$X:=A+(B-A)\tilde{X},\tilde{X}~U([0,1])$$

Uniform Random Vector

When you configure the block to have N > 1 channels, each output sample is a random vector of N independent entries. You can write X as $$X:=\left[\begin{array}{ccc}{X}_1& \cdots & X_N\end{array}\right]$$, where X_k ~ U([A_k,B_k]) with {A₁,…, A_N} and {B₁,…, B_N} are the minimum and the maximum values of the vector parameters, respectively. When you set Samples per frame M > 1, each output frame is an M-by-N matrix of M independent uniform random row vectors.

Complex Uniform Random Variable

When you set the block to generate a complex scalar random variable, X := Y + jZ, where Y, Z ~ U([A, B]).

Alternatively, you can write X as

$$X:=\left(A+jA\right)+(B-A)(\tilde{Y}+j\tilde{Z}),\tilde{Y},\tilde{Z}~U([0,1])$$

Complex Uniform Random Vector

When X is a vector of complex random variables, $$X:=\left[\begin{array}{ccc}{Y}_1+j{Z}_1& \cdots & Y_N+j{Z}_N\end{array}\right]$$, where Y_k, Z_k ~ U([A_k, B_k]) are all independent.

Gaussian Distribution

Scalar Random Variable

When you set the block to generate a random variable from a Gaussian (or normal) distribution, the variable X ~ N(μ,σ²), where μ and σ² are the mean and variance values, respectively.

Alternatively, you can write X as $$X:=\mu +\sigma \tilde{X},\text{where}\tilde{X}~N(0,1)$$ is a standard normal variable.

Gaussian Random Vector

When you set the block to have N > 1 channels, each output sample is a random vector of N independent entries. When X is a Gaussian random vector, $$X:=\left[\begin{array}{ccc}{X}_1& \cdots & X_N\end{array}\right]$$, where X_k ~ N(μ_k, σ_k²), {μ₁, …, μ_N} and {σ₁², …, σ_N²} are the mean and variance values of N channels, respectively. The covariance matrix of the vector X is a diagonal matrix given by $$\left[\begin{array}{ccc}{\sigma }_1{}^2& 0& 0\\ 0& \ddots & 0\\ 0& 0& {\sigma }_N{}^2\end{array}\right]$$.

Complex Gaussian Random Variable

When you set the block to generate a complex scalar random variable, X := Y + jZ, where Y ~ N(Re(μ),(σ²/2)) and Z ~ N(Im(μ),(σ²/2)) are independent. The mean value can be complex.

Alternatively, you can write X as $$X:=\mu +\frac{\sigma }{\sqrt{2}}(\tilde{Y}+j\tilde{Z})$$.

Complex Gaussian Random Vector

When X is a vector of complex random variables, $$X:=\left[\begin{array}{ccc}{Y}_1+j{Z}_1& \cdots & Y_N+j{Z}_N\end{array}\right]$$, where Y_k ~ N(Re(μ_k), (σ_k²/2)) and Z_k ~ N(Im(μ_k), (σ_k²/2)) with {μ₁, …, μ_N} and {σ₁², …, σ_N²} are the mean and variance values of N channels, respectively.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a

R2024a: Random Source block has been updated

The Random Source block has been updated with these changes:

• Support for Mersenne Twister random number generator.

• The Gaussian distribution always uses the Zigguart method. The Sum of uniform values method is no longer supported.

• Repeatable option is removed. To generate a repeatable output, set Repeatability to Specify seed.

• The initial seed must be a scalar. You can no longer specify a vector of seed values.

• When you specify an initial seed, the seed is no longer tunable, that is, you cannot change the value of the seed during simulation.

• The Sample mode parameter is removed. The sample mode of the block is now always discrete.

If you open a model saved in R2023b or a previous version of MATLAB, the model continues to use the older version of the block in R2024a. To use the updated version, obtain the Random Source block from the DSP System Toolbox/Sources library.