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# Standard Deviation

Find standard deviation of input or sequence of inputs

## Library

Statistics

`dspstat3`

## Description

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.

### Basic 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 3-dimensional input signal of size M-by-N-by-P:

• `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 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 input that is an M-by-N matrix, the output at each sample time is an M-by-1 column vector.

```y = std(u,0,2) % Equivalent MATLAB code ```
• `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 input that is an M-by-N matrix, the output at each sample time is a 1-by-N row vector.

```y = std(u,0,1) % Equivalent MATLAB code ```

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 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 M-by-N 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 M-by-N input matrix is the square root of its variance:

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 M-by-N 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.

### Running Operation

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 M-by-N array. Each element yij of the output contains the standard deviation of the element uij over all inputs since the last reset.

• When you select ```Columns as channels (frame based)```, the block outputs an M-by-N matrix. Each element yij of the output contains the standard deviation of the jth column over all inputs since the last reset, up to and including element uij of the current input.

#### Running Operation for Variable-Size Inputs

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.

### Resetting the Running Standard Deviation

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)

• `Non-zero 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 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 in the Simulink Coder™ documentation.

## Examples

In the following ex_standarddeviation_ref model, the Standard Deviation block calculates the running standard deviation of a 3-by-2 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.

## Parameters

Running standard deviation

Enables running operation when selected.

Input processing

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 ```Inherit from input (this choice will be removed - see release notes)``` will be removed in a future release. See Frame-Based Processing in the DSP System Toolbox™ Release Notes for more information.
Reset port

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.

Find the standard deviation value over

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. This parameter appears only when you clear the Running standard deviation check box.

Dimension

Specify the dimension (one-based 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`.

## Supported Data Types

PortSupported Data Types

Input

• Double-precision floating point

• Single-precision floating point

Reset

• Double-precision floating point

• Single-precision floating point

• Boolean

• 8-, 16-, and 32-bit signed integers

• 8-, 16-, and 32-bit unsigned integers

 Mean DSP System Toolbox RMS DSP System Toolbox Variance DSP System Toolbox `std` MATLAB