Standard Deviation

Standard deviation of input or sequence of inputs

• 

Libraries:
DSP System Toolbox / Statistics

Description

The Standard Deviation block computes the standard deviation of each row or column of the input, or along vectors of a specified dimension of the input. It can also compute the standard deviation of the entire input. You can specify the dimension using the Find the standard deviation value over parameter. The Standard Deviation block can also track the standard deviation in a sequence of inputs over a period of time. To track the standard deviation in a sequence of inputs, select the Running standard deviation parameter.

Note

The Running mode in the Standard Deviation block will be removed in a future release. To compute the running standard deviation in Simulink^®, use the Moving Standard Deviation block instead.

Examples

Compute the Standard Deviation

Use the Standard Deviation block to compute the standard deviation.

• Open Model

Compute the Running Standard Deviation

Use the Standard Deviation block to compute the running standard deviation.

• Open Model

Ports

Input

In — Data input

vector | matrix | N-D array

The block accepts real-valued or complex-valued multichannel and multidimensional inputs.

This port is unnamed until you select the Running standard deviation parameter and set the Reset port parameter to any option other than None.

Data Types: single | double
Complex Number Support: Yes

Rst — Reset port

scalar

Specify the reset event that causes the block to reset the running standard deviation. The sample time of the Rst input must be a positive integer multiple of the input sample time.

Dependencies

To enable this port, select the Running standard deviation parameter and set the Reset port parameter to any option other than None.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

Output

Port_1 — Standard deviation along the specified dimension

scalar | vector | matrix | N-D array

The data type of the output matches the data type of the input.

When you do not select the Running standard deviation parameter, the block computes the standard deviation in each row or column of the input, or along vectors of a specified dimension of the input. It can also compute the standard deviation of the entire input at each individual sample time. Each element in the output array y is the standard deviation of the corresponding column, row, or entire input. The output array y depends on the setting of the Find the standard deviation value over parameter. Consider a three-dimensional input signal of size M-by-N-by-P. When you set Find the standard deviation value over to:

• Entire input — The output at each sample time is a scalar that contains the standard deviation of the M-by-N-by-P input matrix.

• Each row — The output at each sample time consists of an M-by-1-by-P array, where each element contains the standard deviation of each vector over the second dimension of the input. For an M-by-N matrix input, the output at each sample time is an M-by-1 column vector.

• Each column — The output at each sample time consists of a 1-by-N-by-P array, where each element contains the standard deviation of each vector over the first dimension of the input. For an M-by-N matrix input, the output at each sample time is a 1-by-N row vector.

  In this mode, the block treats length-M unoriented vector inputs as M-by-1 column vectors.

• Specified dimension — The output at each sample time depends on the value of the Dimension parameter. If you set the Dimension to 1, the output is the same as when you select Each column. If you set the Dimension to 2, the output is the same as when you select Each row. If you set the Dimension to 3, the output at each sample time is an M-by-N matrix containing the standard deviation of each vector over the third dimension of the input.

When you select Running standard deviation, the block tracks the standard deviation of each channel in a time sequence of inputs. In this mode, you must also specify a value for the Input processing parameter.

• Elements as channels (sample based) — The block treats each element of the input as a separate channel. For a three-dimensional input signal of size M-by-N-by-P, the block outputs an M-by-N-by-P array. Each element y_ijk of the output contains the standard deviation of the element u_ijk for all inputs since the last reset.

  When a reset event occurs, the running standard deviation y_ijk in the current frame is reset to the element u_ijk.

• Columns as channels (frame based) — The block treats each column of the input as a separate channel. This option does not support input signals with more than two dimensions. For a two-dimensional input signal of size M-by-N, the block outputs an M-by-N matrix. Each element y_ij of the output contains the standard deviation of the elements in the jth column of all inputs since the last reset, up to and including the element u_ij of the current input.

  When a reset event occurs, the running standard deviation for each channel becomes the standard deviation of all the samples in the current input frame, up to and including the current input sample.

Data Types: single | double

Parameters

Main Tab

Running standard deviation — Option to select running standard deviation

off (default) | on

When you select the Running standard deviation parameter, the block tracks the standard deviation value of each channel in a time sequence of inputs.

Find the standard deviation value over — Dimension over which the block computes the standard deviation

Each column (default) | Entire input | Each row | Specified dimension

• Each column — The block outputs the standard deviation over each column.

• Each row — The block outputs the standard deviation over each row.

• Entire input — The block outputs the standard deviation over the entire input.

• Specified dimension — The block outputs the standard deviation over the dimension, specified in the Dimension parameter.

Dependencies

To enable this parameter, clear the Running standard deviation parameter.

Dimension — Custom dimension

1 (default) | scalar

Specify the dimension (one-based value) of the input signal over which the standard deviation is computed. The value of this parameter must be greater than 0 and less than the number of dimensions in the input signal.

Dependencies

To enable this parameter, set Find the standard deviation value over to Specified dimension.

Input processing — Method to process the input in running mode

Columns as channels (frame based) (default) | Elements as channels (sample based)

• Columns as channels (frame based) — The block treats each column of the input as a separate channel. This option does not support input signals with more than two dimensions. For a two-dimensional input signal of size M-by-N, the block outputs an M-by-N matrix. Each element y_ij of the output contains the standard deviation of the elements in the jth column of all inputs since the last reset, up to and including the element u_ij of the current input.

  When a reset event occurs, the running standard deviation for each channel becomes the standard deviation of all the samples in the current input frame, up to and including the current input sample.

• Elements as channels (sample based) — The block treats each element of the input as a separate channel. For a three-dimensional input signal of size M-by-N-by-P, the block outputs an M-by-N-by-P array. Each element y_ijk of the output contains the standard deviation of the element u_ijk for all inputs since the last reset.

  When a reset event occurs, the running standard deviation y_ijk in the current frame is reset to the element u_ijk.

  Variable-Size Inputs

  When your inputs are of variable size, and you select the Running standard deviation parameter, then:

  • If you set the Input processing parameter to Elements as channels (sample based), the state is reset.

  • If you set the Input processing parameter to Columns as channels (frame based), then:

    • When the input size difference is in the number of channels (number of columns), the state is reset.

    • When the input size difference is in the length of channels (number of rows), no reset occurs and the running operation is carried out as usual.

Dependencies

To enable this parameter, select the Running standard deviation parameter.

Reset port — Reset event

None (default) | Rising edge | Falling edge | Either edge | Non-zero sample

The block resets the running standard deviation whenever a reset event is detected at the optional Rst port. The reset sample time must be a positive integer multiple of the input sample time.

When a reset event occurs while the Input processing parameter is set to Elements as channels (sample based), the running standard deviation for each channel is initialized to the value in the corresponding channel of the current input. Similarly, when the Input processing parameter is set to Columns as channels (frame based), the running standard deviation for each channel becomes the standard deviation of all the samples in the current input frame, up to and including the current input sample.

Use this parameter to specify the reset event.

• None — Disables the Rst port.

• Rising edge — Triggers a reset operation when the Rst input does one of the following:

  • Rises from a negative value to either a positive value or zero.

  • Rises from zero to a positive value, where the rise is not a continuation of a rise from a negative value to zero.

    

• Falling edge — Triggers a reset operation when the Rst input does one of the following:

  • Falls from a positive value to a negative value or zero.

  • Falls from zero to a negative value, where the fall is not a continuation of a fall from a positive value to zero.

    

• Either edge — Triggers a reset operation when the Rst input is a Rising edge or Falling edge.

• Non-zero sample — Triggers a reset operation at each sample time, when the Rst input is not zero.

Note

When running simulations in the Simulink multitasking mode, reset signals have a one-sample latency. Therefore, when the block detects a reset event, there is a one-sample delay at the reset port rate before the block applies the reset. For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Time-Based Scheduling and Code Generation (Simulink Coder).

Dependencies

To enable this parameter, select the Running standard deviation parameter.

Block Characteristics

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

More About

Standard Deviation

The standard deviation of a discrete-time signal is the square root of the variance of the signal.

Standard deviation gives a measure of deviation of the signal from its mean value.

For purely real or imaginary input, u, of size M-by-N, the standard deviation is given by the following equation:

$$y=\sigma =\sqrt{\frac{{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^N{\left|u_{ij}\right|}^2-\frac{{\left|{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^N{u}_{ij}}}\right|}^2}{M*N}}}}{M*N-1}}$$

• u_ij is the input data element at indices i, j.

• M is the length of the jth column.

• N is the number of columns.

For complex inputs, the standard deviation is given by the following equation:

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

• σ_Re² is the variance of the real part of the complex input.

• σ_Im² is the variance of the imaginary part of the complex input.

Algorithms

Standard Deviation

When you clear the Running standard deviation parameter in the block and specify a dimension, the block produces results identical to the MATLAB^® std function, when it is called as y = std(u,0,D).

• u is the data input.

• D is the dimension.

• y is the standard deviation along the specified dimension.

The standard deviation along the entire input is identical to calling the std function as y = std(u(:)).

For a complex input signal, the standard deviation is the square root of the sum of the variances of the real and imaginary parts.

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

Extended Capabilities

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

Version History

Introduced before R2006a