Normalization
Perform vector normalization along rows, columns, or specified dimension
Libraries:
DSP System Toolbox /
Math Functions /
Math Operations
Description
The Normalization block independently normalizes each row, column, or
vector of the specified dimension of the input using the Squared
2norm
or the 2norm
methods.
For more information on how the block normalizes the signal, see Algorithms.
Examples
Ports
Input
Output
Parameters
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

More About
Algorithms
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 given by:
$$Y(i,j,k)=\frac{U(i,j,k)}{V(i,k)+b}$$
In squared 2norm mode, the block output is given by:
$$Y(i,j,k)=\frac{U(i,j,k)}{V{(i,k)}^{2}+b}$$
The normalization bias b is typically chosen to be a small positive constant (for example, 1e10) that prevents potential division by zero.
Extended Capabilities
Version History
Introduced before R2006a