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 2-norm or the 2-norm methods.

For more information on how the block normalizes the signal, see Algorithms.

Examples

Zero Algorithmic Delay

The FFT block is an example of a component that has no algorithmic delay. The Simulink timer does not record any passage of time while the block computes the FFT of the input, and the transformed data is available at the output in the same time step that the input is received. There are many other blocks that have zero algorithmic delay, such as the blocks in the Matrices and Linear Algebra libraries. Each of those blocks processes its input and generates its output in a single time step.

Open Model

Ports

Input

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Input — Input signal
scalar | vector | matrix | N-D array

Specify the input signal as a scalar, vector, matrix, or an N-D array. You can specify both fixed- and floating-point signals in the Squared 2-norm mode but only floating-point signals in the 2-norm mode.

Output

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Output — Normalization output
scalar | vector | matrix | N-D array

Normalized output, returned as a scalar, vector, matrix, or an N-D array. The output always has the same size, data type, and complexity as the input signal.

For more information on how the block normalizes the signal, see Algorithms.

Parameters

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Main Tab

Norm — Normalization type
`Squared 2-norm` (default) | `2-norm`

Specify the type of normalization to perform as one of these:

Squared 2-norm –– Supports both floating-point and fixed-point signals.
2-norm –– Supports only floating-point signals.

Normalization bias — Normalization bias
`1e-10` (default) | nonnegative scalar

Specify the normalization bias as a nonnegative scalar. This is the real value b which the block adds in the denominator to avoid division by zero.

Tunable: Yes

Normalize over — Dimension over which to normalize
`Each column` (default) | `Each row` | `Specified dimension`

Specify the dimension over which to normalize as one of these:

Each column
Each row
Specified dimension –– Use the Dimension parameter to specify the dimension.

Dimension — Specify dimension
`1` (default) | positive integer

Specify the one-based value of the dimension over which to normalize as a positive integer. The value of this parameter cannot exceed the number of dimensions in the input signal.

Dependencies

To enable this parameter, set the Normalize over parameter to Specified dimension.

Data Types Tab

Note

The parameters on this tab are applicable only to fixed-point signals when the block is in squared 2-norm mode. See Fixed-Point Data Types for a diagram of how the product output, accumulator, and output data types are used in this case.

Rounding mode — Rounding mode
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Specify the rounding mode for fixed-point operations as one of the following:

Floor
Ceiling
Convergent
Nearest
Round
Simplest
Zero

For more details, see Rounding Modes.

Saturate on integer overflow — Saturate on integer overflow
`off` (default) | `on`

When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details on saturate and wrap, see overflow mode for fixed-point operations.

Product output — Product output data type
`Inherit: Same as input` (default) | `fixdt([],16,0)`

Specify the product output data type. See Fixed-Point 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 — Accumulator data type
`Inherit: Same as product output` (default) | `Inherit: Same as input` | `fixdt([],16,0)`

Specify the accumulator data type. See Fixed-Point 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 — Output data type
`Inherit: Same as product output` (default) | `Inherit: Same as input` | `Inherit: Same as accumulator` | `fixdt([],16,0)`

Specify the output data type. See Fixed-Point Data Types for illustrations depicting the use of the output 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
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 — Output Minimum
`[]` (default) | scalar

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 fixed-point data types

Output Maximum — Output Maximum
`[]` (default) | scalar

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 fixed-point data types

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in the block dialog box.

Block Characteristics

Data Types	`double` \| `fixed point` \| `integer` \| `single`
Direct Feedthrough	`no`
Multidimensional Signals	`no`
Variable-Size Signals	`yes`
Zero-Crossing Detection	`no`

More About

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Fixed-Point Data Types

This diagram shows the data types used within the Normalization block for fixed-point signals (squared 2-norm 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 box.

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 3-D input U(i,j,k) and assume that you want to normalize along the second dimension. First, define the 2-D intermediate quantity V(i,k) such that each element of V is the norm of one of the vectors in U

$V (i, k) = {(\sum_{j = 1}^{J} U^{2} (i, j, k))}^{1 / 2} .$

Given V, the output of the block Y(i,j,k) in 2-norm mode is given by

$Y (i, j, k) = \frac{U (i, j, k)}{V (i, k) + b} .$

In squared 2-norm 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, 1e-10) that prevents potential division by zero.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a

Normalization

Description

Examples

Zero Algorithmic Delay

Ports

Input

Input — Input signal
scalar | vector | matrix | N-D array

Output

Output — Normalization output
scalar | vector | matrix | N-D array

Parameters

Main Tab

Norm — Normalization type
`Squared 2-norm` (default) | `2-norm`

Normalization bias — Normalization bias
`1e-10` (default) | nonnegative scalar

Normalize over — Dimension over which to normalize
`Each column` (default) | `Each row` | `Specified dimension`

Dimension — Specify dimension
`1` (default) | positive integer

Dependencies

Data Types Tab

Rounding mode — Rounding mode
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Saturate on integer overflow — Saturate on integer overflow
`off` (default) | `on`

Product output — Product output data type
`Inherit: Same as input` (default) | `fixdt([],16,0)`

Accumulator — Accumulator data type
`Inherit: Same as product output` (default) | `Inherit: Same as input` | `fixdt([],16,0)`

Output — Output data type
`Inherit: Same as product output` (default) | `Inherit: Same as input` | `Inherit: Same as accumulator` | `fixdt([],16,0)`

Output Minimum — Output Minimum
`[]` (default) | scalar

Output Maximum — Output Maximum
`[]` (default) | scalar

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

Block Characteristics

More About

Fixed-Point Data Types

Algorithms

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

See Also

Functions

Blocks

Normalization

Description

Examples

Zero Algorithmic Delay

Ports

Input

Input — Input signal scalar | vector | matrix | N-D array

Output

Output — Normalization output scalar | vector | matrix | N-D array

Parameters

Main Tab

Norm — Normalization type Squared 2-norm (default) | 2-norm

Normalization bias — Normalization bias 1e-10 (default) | nonnegative scalar

Normalize over — Dimension over which to normalize Each column (default) | Each row | Specified dimension

Dimension — Specify dimension 1 (default) | positive integer

Dependencies

Data Types Tab

Rounding mode — Rounding mode Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Saturate on integer overflow — Saturate on integer overflow off (default) | on

Product output — Product output data type Inherit: Same as input (default) | fixdt([],16,0)

Accumulator — Accumulator data type Inherit: Same as product output (default) | Inherit: Same as input | fixdt([],16,0)

Output — Output data type Inherit: Same as product output (default) | Inherit: Same as input | Inherit: Same as accumulator | fixdt([],16,0)

Output Minimum — Output Minimum [] (default) | scalar

Output Maximum — Output Maximum [] (default) | scalar

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types off (default) | on

Block Characteristics

More About

Fixed-Point Data Types

Algorithms

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

See Also

Functions

Blocks

Input — Input signal
scalar | vector | matrix | N-D array

Output — Normalization output
scalar | vector | matrix | N-D array

Norm — Normalization type
`Squared 2-norm` (default) | `2-norm`

Normalization bias — Normalization bias
`1e-10` (default) | nonnegative scalar

Normalize over — Dimension over which to normalize
`Each column` (default) | `Each row` | `Specified dimension`

Dimension — Specify dimension
`1` (default) | positive integer

Rounding mode — Rounding mode
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Saturate on integer overflow — Saturate on integer overflow
`off` (default) | `on`

Product output — Product output data type
`Inherit: Same as input` (default) | `fixdt([],16,0)`

Accumulator — Accumulator data type
`Inherit: Same as product output` (default) | `Inherit: Same as input` | `fixdt([],16,0)`

Output — Output data type
`Inherit: Same as product output` (default) | `Inherit: Same as input` | `Inherit: Same as accumulator` | `fixdt([],16,0)`

Output Minimum — Output Minimum
`[]` (default) | scalar

Output Maximum — Output Maximum
`[]` (default) | scalar

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.