Standard Deviation
Standard deviation of input or sequence of inputs
 Library:
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.
Ports
Input
In
— Data input
vector  matrix  ND array
The block accepts realvalued or complexvalued 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  ND 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
threedimensional input signal of size
MbyNbyP.
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 MbyNbyP input matrix.Each row
— The output at each sample time consists of an Mby1byP array, where each element contains the standard deviation of each vector over the second dimension of the input. For an MbyN matrix input, the output at each sample time is an Mby1 column vector.Each column
— The output at each sample time consists of a 1byNbyP array, where each element contains the standard deviation of each vector over the first dimension of the input. For an MbyN matrix input, the output at each sample time is a 1byN row vector.In this mode, the block treats lengthM unoriented vector inputs as Mby1 column vectors.
Specified dimension
— The output at each sample time depends on the value of the Dimension parameter. If you set the Dimension to1
, the output is the same as when you selectEach column
. If you set the Dimension to2
, the output is the same as when you selectEach row
. If you set the Dimension to3
, the output at each sample time is an MbyN 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 threedimensional input signal of size MbyNbyP, the block outputs an MbyNbyP 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 twodimensional input signal of size MbyN, the block outputs an MbyN 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 (onebased 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 twodimensional input signal of size MbyN, the block outputs an MbyN 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 threedimensional input signal of size MbyNbyP, the block outputs an MbyNbyP 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}.
VariableSize 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
 Nonzero 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 aRising edge
orFalling edge
.Nonzero 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 onesample latency. Therefore, when the block detects a reset event, there is a onesample 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 TimeBased Scheduling and Code Generation (Simulink Coder).
Dependencies
To enable this parameter, select the Running standard deviation parameter.
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

More About
Standard Deviation
The standard deviation of a discretetime 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 MbyN, the standard deviation is given by the following equation:
$$y=\sigma =\sqrt{\frac{{\displaystyle \sum _{i=1}^{M}{\displaystyle \sum _{j=1}^{N}{\left{u}_{ij}\right}^{2}\frac{{\left{\displaystyle \sum _{i=1}^{M}{\displaystyle \sum _{j=1}^{N}{u}_{ij}}}\right}^{2}}{M*N}}}}{M*N1}}$$
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_{Re}^{2} is the variance of the real part of the complex input.
σ_{Im}^{2} 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
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