Signal Processing Blockset™

Variance - Compute variance of input or sequence of inputs

Library

Statistics

dspstat3

Description

The Variance block computes the unbiased variance of each row or column of the input, along vectors of a specified dimension of the input, or of the entire input. The Variance block can also track 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 you do not select the Running variance check box, the block computes the variance 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 is the variance of the corresponding column, row, vector, or entire input. The output y depends on the setting of the Find the variance 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 variance of the entire input. In this mode, the output is always sample based.
```
y = var(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 variance 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. In this mode, the frame status of the output is the same as that of the input.
```
y = var(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 variance 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. In this mode, the frame status of the output is the same as that of the input.
```
y = var(u,0,1)					% Equivalent MATLAB code
```
For convenience, length-M 1-D vector inputs are treated as M-by-1 column vectors when the block is in this mode. Sample-based length-M row vector inputs are also treated as M-by-1 column vectors when the Treat sample-based row input as a column check box is selected.
Specified dimension — The output at each sample time depends on Dimension. If Dimension is set to 1, the output is the same as that 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 variance of each vector over the third dimension of the input. In this mode, the frame status of the output is the same as that of the input.
```
y = var(u,0,Dimension)					% Equivalent MATLAB code
```

For purely real or purely imaginary inputs, the variance of an M-by-N matrix is the square of the standard deviation:

For complex inputs, the variance is given by the following equation:

Running Operation

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

N-D signals cannot be frame based. When the block is set to Running mode, each element of the N-D signal is treated as a separate channel. There are channels, where d_i is the size of the ith dimension.

Resetting the Running Variance

The block resets the running variance 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 the topic on models with multiple sample rates in the Real-Time Workshop documentation.

ROI Processing

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 variance value over parameter is set to Entire input and the Running variance check box is not selected. ROI processing is only supported for 2-D inputs.

Note Full ROI processing is only available to users who have a Video and Image Processing Blockset license. If you only have a Signal Processing Blockset license, you can still use ROI processing, but are limited to the ROI type Rectangles.

Use the ROI type parameter to specify whether the ROI is a binary mask, label matrix, rectangle, or line. ROI processing is only supported for 2-D inputs.

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 reference page.

Note 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.

Fixed-Point Data Types

The parameters on the Fixed-Point pane of the block dialog are only used for fixed-point inputs. For purely real or purely imaginary inputs, the variance of the input is the square of its standard deviation. For complex inputs, the output is the sum of the variance of the real and imaginary parts of the input.

The following diagram shows the data types used within the Variance block for fixed-point signals.

The results of the magnitude-squared calculations in the figure are in the product output data type. You can set the accumulator, product output, and output data types in the block dialog as discussed in Dialog Box.

Examples

The Variance block in the next model 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 = dsp_examples_u
Sample time = 1/3
Samples per frame = 3

where

dsp_examples_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 next figure shows the block's operation.

Dialog Box

The Main pane of the Variance block dialog appears as follows.

Running variance

Enables running operation when selected.

Reset port

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

Find the variance value over

Specify whether to find the variance along rows, columns, entire input, or the dimension specified in the Dimension parameter. For more information, see Basic Operation.

Treat sample-based row input as a column

Select to treat sample-based length-M row vector inputs as M-by-1 column vectors. This parameter is only visible when the Find the variance value over parameter is set to Each column.

Dimension

Specify the dimension (one-based value) of the input signal, over which the variance 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 variance value over parameter is set to Specified dimension.

Enable ROI Processing

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 variance value over parameter is set to Entire input, and the block is not in running mode.

ROI type

Specify the type of ROI you want to use. Your choices are Rectangles, Lines, Label matrix, or Binary mask.

ROI portion to process

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.

Output

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

If you select this check box, the Flag port appears on the block. For a description of the Flag port output, see the tables in ROI Processing. This parameter is visible if, for the ROI type parameter, you select Rectangles or Lines.

Output flag indicating if label numbers are valid

The Fixed-point pane of the Variance block dialog appears as follows.

Rounding mode

Select the rounding mode for fixed-point operations.

Overflow mode

Select the overflow mode for fixed-point operations.

Note See Fixed-Point Data Types for more information on how the product output, accumulator, and output data types are used in this block.

Input-squared product

Use this parameter to specify how to designate the input-squared product word and fraction lengths:

When you select Same as input, these characteristics match those of the input to the block.
When you select Binary point scaling, you can enter the word length and the fraction length of the input-squared product, in bits.
When you select Slope and bias scaling, you can enter the word length, in bits, and the slope of the input-squared product. This block requires power-of-two slope and a bias of zero.

Input-sum-squared product

Use this parameter to specify how to designate the input-sum-squared product word and fraction lengths:

When you select Same as input-squared product, these characteristics match those of the input-squared product.
When you select Binary point scaling, you can enter the word length and the fraction length of the input-sum-squared product, in bits.
When you select Slope and bias scaling, you can enter the word length, in bits, and the slope of the input-sum-squared product. This block requires power-of-two slope and a bias of zero.

Accumulator

Use this parameter to specify the accumulator word and fraction lengths resulting from a complex-complex multiplication in the block:

When you select Same as input-squared product, these characteristics match those of the input-squared product.
When you select Same as input, these characteristics match those of the input to the block.
When you select Binary point scaling, you can enter the word length and the fraction length of the accumulator, in bits.
When you select Slope and bias scaling, you can enter the word length, in bits, and the slope of the accumulator. This block requires power-of-two slope and a bias of zero.