Find standard deviation of input or sequence of inputs
Statistics
dspstat3
The Standard Deviation block computes the standard deviation of each row or column of the input, along vectors of a specified dimension of the input, or of the entire input. The Standard Deviation block can also track the standard deviation of a sequence of inputs over a period of time. The Running standard deviation parameter selects between basic operation and running operation.
When you do not select the Running standard deviation check box, the block computes the standard deviation of each row or column of the input, along vectors of a specified dimension of the input, or of the entire input at each individual sample time, and outputs the array y. Each element in y contains the standard deviation of the corresponding column, row, vector, or entire input. The output y depends on the setting of the Find the standard deviation value over parameter. For example, consider a 3dimensional input signal of size MbyNbyP:
Entire input
— The
output at each sample time is a scalar that contains the standard
deviation of the entire input.
y = std(u(:)) % Equivalent MATLAB code
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 input that is an MbyN matrix,
the output at each sample time is an Mby1 column
vector.
y = std(u,0,2) % Equivalent MATLAB code
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 input that is an MbyN matrix,
the output at each sample time is a 1byN row
vector.
y = std(u,0,1) % Equivalent MATLAB code
In this mode, the block treats lengthM unoriented vector inputs as Mby1 column vectors.
Specified Dimension
—
The output at each sample time depends on Dimension.
If Dimension is set to 1
,
the output is the same as when you select Each column
.
If Dimension is set to 2
,
the output is the same as when you select Each row
.
If Dimension is set to 3
,
the output at each sample time is an MbyN matrix
containing the standard deviation of each vector over the third dimension
of the input.
y = std(u,0,Dimension) % Equivalent MATLAB code
For purely real or purely imaginary inputs, the standard deviation of the jth column of an MbyN input matrix is the square root of its variance:
$$\begin{array}{cc}{y}_{j}={\sigma}_{j}=\sqrt{\frac{{\displaystyle \sum _{i=1}^{M}{\left{u}_{ij}{\mu}_{j}\right}^{2}}}{M1}}\text{}& 1\le j\le N\end{array}$$
For complex inputs, the output is the total standard deviation, which equals the square root of the total variance, or the square root of the sum of the variances of the real and imaginary parts. The standard deviation of each column in an MbyN input matrix is given by:
$${\sigma}_{j}=\sqrt{{\sigma}_{j,\mathrm{Re}}^{2}+{\sigma}_{j,\mathrm{Im}}^{2}}$$
Note: The total standard deviation does not equal the sum of the real and imaginary standard deviations. 
When you select the Running standard deviation check box, the block tracks the standard deviation of successive inputs to the block. In this mode, you must also specify a value for the Input processing parameter:
When you select Elements as channels
(sample based)
, the block outputs an MbyN array.
Each element y_{ij} of the
output contains the standard deviation of the element u_{ij} over
all inputs since the last reset.
When you select Columns as channels (frame
based)
, the block outputs an MbyN matrix.
Each element y_{ij} of the
output contains the standard deviation of the jth
column over all inputs since the last reset, up to and including element u_{ij} of
the current input.
When your inputs are of variable size, and you select the Running standard deviation check box, there are two options:
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
there are two cases:
When the input size difference is in the number of channels (i.e., number of columns), the state is reset.
When the input size difference is in the length of channels (i.e., number of rows), there is no reset and the running operation is carried out as usual.
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.
You specify the reset event in the Reset port parameter:
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 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 (see the following figure)
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 (see the following figure)
Either edge
— Triggers
a reset operation when the Rst
input is a Rising
edge
or Falling edge
(as
described earlier)
Nonzero sample
—
Triggers a reset operation at each sample time that 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 in the Simulink Coder™ documentation. 
To calculate the statistical value within a particular region
of interest (ROI) of the input, select the Enable ROI processing check
box. This option is only available when the Find the standard
deviation value over parameter is set to Entire
input
and the Running standard deviation check
box is not selected. ROI processing is only supported for 2D inputs.
Note:
Full ROI processing is available only if you have a Computer Vision System Toolbox™ license.
If you do not have a Computer Vision System Toolbox license,
you can still use ROI processing, but are limited to the ROI
type 
Use the ROI type parameter to specify whether
the ROI is a rectangle, line, label matrix, or binary mask. A binary
mask is a binary image that enables you to specify which pixels to
highlight, or select. In a label matrix, pixels equal to 0 represent
the background, pixels equal to 1 represent the first object, pixels
equal to 2 represent the second object, and so on. When the ROI
type parameter is set to Label matrix
,
the Label and Label Numbers ports appear on the block. Use the Label
Numbers port to specify the objects in the label matrix for which
the block calculates statistics. The input to this port must be a
vector of scalar values that correspond to the labeled regions in
the label matrix. For more information about the format of the input
to the ROI port when the ROI is a rectangle or a line, see the Draw Shapes block reference page.
For rectangular ROIs, use the ROI portion to process parameter to specify whether to calculate the statistical value for the entire ROI or just the ROI perimeter.
Use the Output parameter to specify the
block output. The block can output separate statistical values for
each ROI or the statistical value for all specified ROIs. This parameter
is not available if, for the ROI type parameter,
you select Binary mask
.
If, for the ROI type parameter, you select Rectangles
or Lines
,
the Output flag indicating if ROI is within image bounds check
box appears in the dialog box. If you select this check box, the Flag
port appears on the block. The following tables describe the Flag
port output based on the block parameters.
Output = Individual statistics for each ROI
Flag Port Output  Description 

0  ROI is completely outside the input image. 
1  ROI is completely or partially inside the input image. 
Output = Single statistic for all ROIs
Flag Port Output  Description 

0  All ROIs are completely outside the input image. 
1  At least one ROI is completely or partially inside the input image. 
If the ROI is partially outside the image, the block only computes the statistical values for the portion of the ROI that is within the image.
If, for the ROI type parameter, you select Label
matrix
, the Output flag indicating if input
label numbers are valid check box appears in the dialog
box. If you select this check box, the Flag port appears on the block.
The following tables describe the Flag port output based on the block
parameters.
Output = Individual statistics for each ROI
Flag Port Output  Description 

0  Label number is not in the label matrix. 
1  Label number is in the label matrix. 
Output = Single statistic for all ROIs
Flag Port Output  Description 

0  None of the label numbers are in the label matrix. 
1  At least one of the label numbers is in the label matrix. 
In the following ex_standarddeviation_refex_standarddeviation_ref model,
the Standard Deviation block calculates the running standard deviation
of a 3by2 matrix input, u
. The Input
processing parameter is set to Columns as
channels (frame based)
, so the block processes the input
as a two channel signal with a frame size of three. The running standard
deviation is reset at t=2 by an impulse to the
block's Rst
port.
The operation of the block is shown in the following figure.
Enables running operation when selected.
Specify how the block should process the input when computing the running standard deviation. You can set this parameter to one of the following options:
Columns as channels (frame based)
—
When you select this option, the block treats each column of the input
as a separate channel.
Elements as channels (sample based)
—
When you select this option, the block treats each element of the
input as a separate channel.
This parameter appears only when you select the Running standard deviation check box.
Note:
The option 
Specify the reset event that causes the block to reset the running standard deviation. The sample time of the input to the Rst port must be a positive integer multiple of the input sample time. This parameter appears only when you select the Running standard deviation check box. For more information, see Resetting the Running Standard Deviation.
Specify whether to find the standard deviation value along rows, columns, entire input, or the dimension specified in the Dimension parameter. For more information, see Basic Operation.
Select to treat samplebased lengthM row
vector inputs as Mby1 column vectors. This parameter
is only visible when the Find the standard deviation value
over parameter is set to Each column
.
Note: This check box will be removed in a future release. See SampleBased Row Vector Processing Changes for more information. 
Specify the dimension (onebased value) of the input signal,
over which the standard deviation is computed. The value of this parameter
cannot exceed the number of dimensions in the input signal. This parameter
is only visible when the Find the standard deviation value
over parameter is set to Specified dimension
.
Select this check box to calculate the statistical value within
a particular region of each image. This parameter is only available
when the Find the standard deviation value over parameter
is set to Entire input
, and the block is
not in running mode.
Note
Full ROI processing is available only when you have a Computer Vision System Toolbox license.
If you do not have a Computer Vision System Toolbox license,
you can still use ROI processing, but are limited to the ROI
type 
Specify the type of ROI you want to use. Your choices are Rectangles
, Lines
, Label
matrix
, or Binary mask
.
Specify whether you want to calculate the statistical value
for the entire ROI or just the ROI perimeter. This parameter is only
visible if, for the ROI type parameter, you specify Rectangles
.
Specify the block output. The block can output a vector of separate
statistical values for each ROI or a scalar value that represents
the statistical value for all the specified ROIs. This parameter is
not available if, for the ROI type parameter,
you select Binary mask
.
Output flag indicating if ROI is within image bounds
Output flag indicating if label numbers are valid
When you select either of these check boxes, the Flag port appears on the block. For a description of the Flag port output, see the tables in ROI Processing.
The Output flag indicating if ROI is within image
bounds check box is only visible when you select Rectangles
or Lines
as
the ROI type.
The Output flag indicating if label numbers are valid check
box is only visible when you select Label matrix
for
the ROI type parameter.
Port  Supported Data Types 

Input 

Reset 

ROI  Rectangles and lines:
Binary Mask:

Label 

Label Numbers 

Output 

Flag 
