Normalization
Perform vector normalization along rows, columns, or specified dimension
Library
Math Functions / Math Operations
dspmathops
Description
The Normalization block independently normalizes each row, column, or vector of the specified dimension of the input. The block accepts both fixed and floatingpoint signals in the squared 2norm mode, but only floatingpoint signals in the 2norm mode. The output always has the same dimensions as the input.
This block treats an arbitrarily dimensioned input U as a collection of vectors oriented along the specified dimension. The block normalizes these vectors by either their norm or the square of their norm.
For example, consider a 3dimensional input U(i,j,k) and assume that you want to normalize along the second dimension. First, define the 2dimensional intermediate quantity V(i,k) such that each element of V is the norm of one of the vectors in U:
$$V(i,k)={\left({\displaystyle \sum _{j=1}^{J}{U}^{2}(i,j,k)}\right)}^{1/2}$$
Given V, the output of the block Y(i, j,k) in 2norm mode is
$$Y(i,j,k)=\frac{U(i,j,k)}{V(i,k)+b}$$
In squared 2norm mode, the block output is
$$Y(i,j,k)=\frac{U(i,j,k)}{V{(i,k)}^{2}+b}$$
The normalization bias, b, is typically chosen to be a small positive constant (for example, 1e10) that prevents potential division by zero.
FixedPoint Data Types
The following diagram shows the data types used within the Normalization block for fixedpoint signals (squared 2norm mode only).
The output of the multiplier is in the product output data type when the input is real. When the input is complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, see Multiplication Data Types. You can set the accumulator, product output, and output data types in the block dialog as discussed in Parameters.
Examples
See Zero Algorithmic Delay in the DSP System Toolbox™ User's Guide for an example.
Parameters
Main Tab
 Norm
Specify the type of normalization to perform,
2norm
orSquared 2norm
.2norm
mode supports floatingpoint signals only.Squared 2norm
supports both fixedpoint and floatingpoint signals. Normalization bias
Specify the real value b to be added in the denominator to avoid division by zero. Tunable (Simulink).
 Normalize over
Specify whether to normalize along rows, columns, or the dimension specified in the Dimension parameter.
 Dimension
Specify the onebased value of the dimension over which to normalize. The value of this parameter cannot exceed the number of dimensions in the input signal. This parameter is only visible if
Specified dimension
is selected for the Normalize over parameter.
Data Types Tab
Note
The parameters on this pane are only applicable to fixedpoint signals when the block is in squared 2norm mode. See FixedPoint Data Types for a diagram of how the product output, accumulator, and output data types are used in this case.
 Rounding mode
Specify the rounding mode for fixedpoint operations as one of the following:
Floor
Ceiling
Convergent
Nearest
Round
Simplest
Zero
For more details, see rounding mode.
 Saturate on integer overflow
When you select this parameter, the block saturates the result of its fixedpoint operation. When you clear this parameter, the block wraps the result of its fixedpoint operation. For details on
saturate
andwrap
, see overflow mode for fixedpoint operations. Product output
Specify the product output data type. See FixedPoint Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it to:
A rule that inherits a data type, for example,
Inherit: Same as input
An expression that evaluates to a valid data type, for example,
fixdt([],16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
 Accumulator
Specify the accumulator data type. See FixedPoint Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:
A rule that inherits a data type, for example,
Inherit: Same as product output
A rule that inherits a data type, for example,
Inherit: Same as input
An expression that evaluates to a valid data type, for example,
fixdt([],16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
 Output
Specify the output data type. See FixedPoint Data Types for illustrations depicting the use of the output data type in this block. You can set it to:
A rule that inherits a data type, for example,
Inherit: Same as product output
A rule that inherits a data type, for example,
Inherit: Same as input
A rule that inherits a data type, for example,
Inherit: Same as accumulator
An expression that evaluates to a valid data type, for example,
fixdt([],16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.
See Control Data Types of Signals (Simulink) for more information.
 Output Minimum
Specify the minimum value that the block should output. The default value is
[]
(unspecified). Simulink^{®} software uses this value to perform:Simulation range checking (see Specify Signal Ranges (Simulink))
Automatic scaling of fixedpoint data types
 Output Maximum
Specify the maximum value that the block should output. The default value is
[]
(unspecified). Simulink software uses this value to perform:Simulation range checking (see Specify Signal Ranges (Simulink))
Automatic scaling of fixedpoint data types
 Lock data type settings against changes by the fixedpoint tools
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block mask.
Supported Data Types
Port  Supported Data Types 

Input 

Output 
