DSP Blockset

Standard Deviation

Find the standard deviation of an input or sequence of inputs.

Library

Statistics

Description

The Standard Deviation block computes the standard deviation of each column in the input, or tracks 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 the Running standard deviation check box is not selected, the block computes the standard deviation of each column in M-by-N input matrix u independently at each sample time.

• y = std(u)           % Equivalent MATLAB code
  

For convenience, length-M 1-D vector inputs and sample-based length-M row vector inputs are both treated as M-by-1 column vectors. (A scalar input generates a zero-valued output.)

The output at each sample time, y, is a 1-by-N vector containing the standard deviation for each column in u. For purely real or purely imaginary inputs, the standard deviation of the jth column is the square root of the variance

where µ_j is the mean of jth column. For complex inputs, the output is the total standard deviation for each column in u, which is the square root of the total variance for that column.

Note that the total standard deviation is not equal to the sum of the real and imaginary standard deviations. The frame status of the output is the same as that of the input.

Running Operation

When the Running standard deviation check box is selected, the block tracks the standard deviation of each channel in a time-sequence of M-by-N inputs. For sample-based inputs, the output is a sample-based M-by-N matrix with each element y_ij containing the standard deviation of element u_ij over all inputs since the last reset. For frame-based inputs, the output is a frame-based M-by-N matrix with each element y_ij containing 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.

As in basic operation, length-M 1-D vector inputs and sample-based length-M row vector inputs are both treated as M-by-1 column vectors.

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 signal rate must be a positive integer multiple of the rate of the data signal input.

The reset event is specified by the Reset port parameter, and can be one of the following:

• 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 above).
• 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, sample-based reset signals have a one-sample latency, and frame-based reset signals have one frame of latency. Thus, there is a one-sample or one-frame delay between the time the block detects a reset event, and when it applies the reset. For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and the topic on the Simulation Parameters dialog box in the Simulink documentation.

Example

The Standard Deviation block in the model below calculates the running standard deviation of a frame-based 3-by-2 (two-channel) matrix input, u. The running standard deviation is reset at t=2 by an impulse to the block's Rst port.

The Standard Deviation block has the following settings:

• Running standard deviation =
• Reset port = Non-zero sample

The Signal From Workspace block has the following settings:

• Signal = u
• Sample time = 1/3
• Samples per frame = 3

where

• u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 1 6 2 5 0 4 17]'
  

The Discrete Impulse block has the following settings:

• Delay (samples) = 2
• Sample time = 1
• Samples per frame = 1

The block's operation is shown in the figure below.

Dialog Box

Running standard deviation

Enables running operation when selected.

Reset port

Determines the reset event that causes the block to reset the running standard deviation. The reset signal rate must be a positive integer multiple of the rate of the data signal input. This parameter is enabled only when you set the Running standard deviation parameter. For more information, see Resetting the Running Standard Deviation.

Supported Data Types

• Double-precision floating point
• Single-precision floating point
• Boolean -- The block accepts Boolean inputs to the Rst port.

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Mean	DSP Blockset
RMS	DSP Blockset
Variance	DSP Blockset
std	MATLAB

Also see Statistics for a list of all the blocks in the Statistics library.

Stack

Submatrix