Perform vector normalization along rows, columns, or specified dimension
Math Functions / Math Operations
dspmathops
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.
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 Dialog Box.
See Zero Algorithmic Delay in the DSP System Toolbox™ User's Guide for an example.
The Main pane of the Normalization dialog appears as follows.
Specify the type of normalization to perform, 2norm
or Squared
2norm
. 2norm
mode supports
floatingpoint signals only. Squared 2norm
supports
both fixedpoint and floatingpoint signals.
Specify the real value b to be added in the denominator to avoid division by zero. Tunable.
Specify whether to normalize along rows, columns, or the dimension specified in the Dimension parameter.
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.
The Data Types pane of the Normalization dialog appears as follows.
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. 
Select the rounding mode for fixedpoint operations.
Select the overflow mode for fixedpoint operations.
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 data type parameter.
See Specify Data Types Using Data Type Assistant for more information.
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
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 data type parameter.
See Specify Data Types Using Data Type Assistant for more information.
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
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 data type parameter.
See Control Signal Data Types for more information.
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 Signal Ranges)
Automatic scaling of fixedpoint data types
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 Signal Ranges)
Automatic scaling of fixedpoint data types
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block mask.
Port  Supported Data Types 

Input 

Output 

ArrayVector Multiply  DSP System Toolbox 
Reciprocal Condition  DSP System Toolbox 
norm  MATLAB 