Median

Median value of input

• 

Libraries:
DSP System Toolbox / Statistics

Description

The Median block computes the median of each row or column of the input, or along vectors of a specified dimension of the input. It can also compute the median of the entire input. You can specify the dimension using the Find the median value over parameter. While computing the median, the block first sorts the input values. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values. To sort the data, you can specify the Sort algorithm parameter as either Quick sort or Insertion sort. The block sorts complex inputs according to their magnitude.

Ports

Input

Port_1 — Data input

vector | matrix | N-D array

The block accepts real-valued or complex-valued multichannel and multidimensional inputs. The input data type must be double precision, single precision, integer, or fixed point, with power-of-two slope and zero bias.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point
Complex Number Support: Yes

Output

Port_1 — Median value along specified dimension

vector | matrix | N-D array

The block computes the median value in each row or column of the input, or along vectors of a specified dimension of the input. It can also compute the median of the entire input. Each element in the output array y is the median value of the corresponding column, row, or entire input. The output array y depends on the setting of the Find the median value over parameter.

Consider a three-dimensional input signal of size M-by-N-by-P. When you set Find the median value over to:

• Entire input — The output at each sample time is a scalar that contains the median value of the M-by-N-by-P input matrix.

• Each row — The output at each sample time consists of an M-by-1-by-P array, where each element contains the median value of each vector over the second dimension of the input. For an M-by-N matrix input, the output is an M-by-1 column vector.

• Each column — The output at each sample time consists of a 1-by-N-by-P array, where each element contains the median value of each vector over the first dimension of the input. For an M-by-N matrix input, the output at each sample time is a 1-by-N row vector.

  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 the value of the Dimension parameter. If you set the Dimension to 1, the output is the same as when you select Each column. If you set the Dimension to 2, the output is the same as when you select Each row. If you set the Dimension to 3, the output at each sample time is an M-by-N matrix containing the median value of each vector over the third dimension of the input.

  The data type of the output matches the data type of the input.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point
Complex Number Support: Yes

Parameters

Main Tab

Sort algorithm — Sort method

Quick sort (default) | Insertion sort

Specify the sorting algorithm as either Quick sort or Insertion sort.

Find the median value over — Dimension over which the median is computed

Each column (default) | Entire input | Each row | Specified dimension

• Each column — The block outputs the median value over each column.

• Each row — The block outputs the median value over each row.

• Entire input — The block outputs the median value over the entire input.

• Specified dimension — The block outputs the median value over the dimension specified in the Dimension parameter.

Dimension — Custom dimension

1 (default) | scalar

Specify the dimension (one-based value) of the input signal over which the block computes the median. The value of this parameter must be greater than 0 and less than or equal to the number of dimensions in the input signal.

Dependencies

To enable this parameter, set Find the median value over to Specified dimension.

Data Types Tab

Note

To use these parameters, the data input must be fixed point. For all other inputs, the parameters on the Data Types tab are ignored.

Rounding mode — Method of rounding operation

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Specify the rounding mode for fixed-point operations. For more details, see rounding mode.

Saturate on integer overflow — Method of overflow action

off (default) | on

When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details on saturate and wrap, see overflow mode for fixed-point operations.

Product output — Product output data type

Inherit: Same as input (default) | fixdt([],16,0)

Specify the data type of the output of a product operation in the Median block. For more information, see Fixed-Point Data Types and Multiplication Data Types.

You can set this parameter to:

• Inherit: Same as input — The product output data type is the same as the input data type.

• fixdt([],16,0) — The product output data type is an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Product output data type by using the Data Type Assistant. To use the assistant, click the Show data type assistant button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

Accumulator — Accumulator data type

Inherit: Same as product output (default) | Inherit: Same as input | fixdt([],16,0)

Specify the data type of the output of an accumulation operation in the Median block. For more details, see Fixed-Point Data Types.

You can set this parameter to:

• Inherit: Same as product output — The accumulator data type is the same as the product output data type.

• Inherit: Same as input — The accumulator data type is the same as the input data type.

• fixdt([],16,0) — The accumulator data type is an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Accumulator data type by using the Data Type Assistant. To use the assistant, click the Show data type assistant button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

Output — Output data type

Inherit: Same as accumulator (default) | Inherit: Same as input | Inherit: Same as product output | fixdt([],16,0)

Output specifies the data type of the output of the Median block. For more details, see Fixed-Point Data Types.

You can set this parameter to:

• Inherit: Same as accumulator — The output data type is the same as the accumulator data type.

• Inherit: Same as input — The output data type is the same as the input data type.

• Inherit: Same as product output — The output data type is the same as the product output data type.

• fixdt([],16,0) — The output data type is an autosigned, binary-point, scaled, fixed-point data type with a word length of 16 bits and a fraction length of 0.

Alternatively, you can set the Output data type by using the Data Type Assistant. To use the assistant, click the Show data type assistant button.

For more information on the data type assistant, see Specify Data Types Using Data Type Assistant (Simulink).

Output Minimum — Minimum output value

[] (default) | scalar

Specify the minimum value that the block can output. The default value is [] (unspecified). Simulink^® uses this value to perform:

• Simulation range checking. See Specify Signal Ranges (Simulink).

• Automatic scaling of fixed-point data types.

Output Maximum — Maximum output value

[] (default) | scalar

Specify the maximum value that the block can output. The default value is [] (unspecified). Simulink uses this value to perform:

• Simulation range checking. See Specify Signal Ranges (Simulink).

• Automatic scaling of fixed-point data types.

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the data types you specify on the block.

Block Characteristics

Data Types	double | fixed point | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	yes
Zero-Crossing Detection	no

More About

Fixed-Point Data Types

For fixed-point inputs, you can specify the Accumulator, Product output, and Output data types in the block dialog box. Not all of these fixed-point parameters are applicable to all types of fixed-point inputs. The table shows when each kind of data type and scaling is used.

M is the length of the sorted data along the specified dimension. X indicates that the particular data type is applicable.

	Output data type	Accumulator data type	Product output data type
Even M	X	X	Not Applicable
Odd M	X	Not Applicable	Not Applicable
Odd M and complex	X	X	X
Even M and complex	X	X	X

When M is even, the Accumulator and Output data types and scalings are used for fixed-point signals. While calculating the average of the two central rows of the input matrix, the result of the sum is stored in the Accumulator data type and scaling. The total result of the average, which is the median of the data, is stored in the Output data type and scaling.

When the fixed-point inputs are complex, both the Accumulator and the Product output data types are used in addition to the Output data type. Before sorting the data, the block computes the sum of the squares of the real and imaginary components of the complex input. The results of the squares are stored in the Product output data type and scaling. The result of the sum of the squares is stored in the Accumulator data type and scaling.

For fixed-point inputs that are both complex and have even M, the Accumulator data type also stores the sum of the two central rows of the input matrix. The average of the two central rows, which is the median of the data, is stored in the Output data type.

Algorithms

Median

The median of a set of data is calculated using the following steps:

1. The values are sorted using the specified sorting algorithm.

2. If the number of values is odd, the median is the middle value.

3. If the number of values is even, the median is the average of the two middle values.

The block produces results identical to the MATLAB^® median function when called as y = median(u,D), where

• u is the data input.

• D is the dimension.

• y is the median value.

When the block calculates the median value along the entire input, the result is identical to calling the median function as y = median(u(:)).

When the input is complex, the block sorts the data according to the magnitude of each value. The magnitude in this case is defined as the sum of the squares of the real and imaginary components of the complex input.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a