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.

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

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

Dialog Box

Norm

The type of normalization to apply, 2-norm or Squared 2-norm. Tunable, except in Simulink's external mode.

Normalization bias

The value b to be added in the denominator to avoid division by zero. Tunable, except in Simulink's external mode.

See Also

Matrix Scaling	DSP Blockset
Reciprocal Condition	DSP Blockset
norm	MATLAB

N-Sample Switch

Overlap-Add FFT Filter