DSP Blockset

Normalization

Normalize an input by its 2-norm or squared 2-norm.

Library

Math Functions / Math Operations

Description

The Normalization block independently normalizes each column of the M-by-N matrix input, u.

The block accepts the following types of inputs:

• Frame-based vectors and matrices
• Sample-based row and column vectors
• Sample-based unoriented (1-D) vectors

Note the block does not accept sample-based full matrix inputs.

The output always has the same dimension and frame status as the input. For convenience, length-M 1-D vectors and sample-based length-M row vectors are both treated as M-by-1 column vectors.

2-Norm

When the Norm parameter specifies 2-norm, the block normalizes the jth input column as follows.

where b is specified by the Normalization bias parameter, and is the 2-norm (or Euclidean norm) of the jth input column.

Equivalently,

• y = u ./ (norm(u) + b)        % Equivalent MATLAB code
  

The normalization bias, b, is typically chosen to be a small positive constant (e.g., 1e-10) that prevents potential division by zero.

Squared 2-Norm

When the Norm parameter specifies Squared 2-norm, the block normalizes the jth input column as follows.

where

Equivalently,

• y = u ./ (norm(u).^2 + b)     % Equivalent MATLAB code
  

Dialog Box

Norm

The type of normalization to apply, 2-norm or Squared 2-norm. Tunable in simulation.

Normalization bias

The real value b to be added in the denominator to avoid division by zero. Tunable in simulation.

Supported Data Types

• Double-precision floating point
• Single-precision floating point

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Matrix Scaling	DSP Blockset
Reciprocal Condition	DSP Blockset
norm	MATLAB

Also see Math Operations for a list of all the blocks in the Math Operations library.

N-Sample Switch

Overlap-Add FFT Filter