DSP Blockset

Variance

Compute the variance of an input or sequence of inputs.

Library

Statistics

Description

The Variance block computes the variance of each column in the input, or tracks the variance of a sequence of inputs over a period of time. The Running variance parameter selects between basic operation and running operation.

Basic Operation

When the Running variance check box is not selected, the block computes the variance of each column in M-by-N input matrix u independently at each sample time.

y = var(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 variance for each column in u. For purely real or purely imaginary inputs, the variance of the jth column is the square of the standard deviation:

where µ_j is the mean of the jth column. For complex inputs, the output is the total variance for each column in u, which is the sum of the real and imaginary variances for that column:

The frame status of the output is the same as that of the input.

Running Operation

When the Running variance check box is selected, the block tracks the variance 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 yij containing the variance of element uij over all inputs since the last reset. For frame-based inputs, the output is a frame-based M-by-N matrix with each element yij containing the variance of the jth column over all inputs since the last reset, up to and including element uij of the current input.

If the Reset port parameter is set to Non-zero sample, the optional Rst port is enabled and the block resets the running variance when the scalar input at the Rst port is nonzero. (The Rst port can be disabled by setting the Reset port parameter to None.)

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.

Example

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

The Variance block has the following settings:

• Running variance =
• 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.

The statsdem demo illustrates the operation of several blocks from the Statistics library.

Dialog Box

Running variance

Enables running operation when selected.

Reset port

Enables the Rst input port when set to Non-zero sample, and disables the Rst input port when set to None.

See Also

Mean	DSP Blockset
RMS	DSP Blockset
Standard Deviation	DSP Blockset
var	MATLAB

Variable Selector

Vector Scope