Implement discrete transfer function

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Libraries:
Simulink / Discrete
HDL Coder / Discrete
HDL Coder / HDL Floating Point Operations

Description

The Discrete Transfer Fcn block implements the z-transformtransfer function as follows:

$H (z) = \frac{n u m (z)}{d e n (z)} = \frac{n u m_{0} z^{m} + n u m_{1} z^{m - 1} + ... + n u m_{m}}{d e n_{0} z^{n} + d e n_{1} z^{n - 1} + ... + d e n_{n}}$

where m+1 and n+1 are the number of numerator and denominator coefficients,respectively. num and den contain the coefficientsof the numerator and denominator in descending powers of z.num can be a vector or matrix, while den mustbe a vector. The order of the denominator must be greater than or equal to the order ofthe numerator.

Specify the coefficients of the numerator and denominator polynomials in descending powersof z. This block lets you use polynomials in z torepresent a discrete system, a method that control engineers typically use. Conversely,the Discrete Filter block lets you use polynomials inz^-1 (the delay operator) torepresent a discrete system, a method that signal processing engineers typically use.The two methods are identical when the numerator and denominator polynomials have thesame length.

The Discrete Transfer Fcn block applies the z-transformtransfer function to each independent channel of the input. The Inputprocessing parameter allows you to specify whether the block treats eachcolumn of the input as an individual channel (frame-based processing) or each element ofthe input as an individual channel (sample-based processing). To perform frame-basedprocessing, you must have a DSP System Toolbox™ license.

Specifying Initial States

Use the Initial states parameter to specify the initial filter states.The initial states you specify are the initial conditions of the unit delay blocksthat are used in the filter digram implementing the discrete transferfunction.

To determine the number of initial states you must specify and how to specifythem, use the following tables.

Frame-Based Processing

Input	Number of Channels	Valid Initial States (Dialog Box)	Valid Initial States (Input Port)
Column vector (K-by-1) Unoriented vector (K)	1	Scalar Column vector (M-by-1) Row vector (1-by-M)	Scalar Column vector (M-by-1)
Row vector (1-by-N) Matrix (K-by-N)	N	Scalar Column vector (M-by-1) Row vector (1-by-M) Matrix (M-by-N)	Scalar Matrix (M-by-N)

Sample-Based Processing

Input	Number of Channels	Valid Initial States (Dialog Box)	Valid Initial States (Input Port)
Scalar	1	Scalar Column vector (M-by-1) Row vector (1-by-M)	Scalar Column vector (M-by-1) Row vector (1-by-M)
Row vector (1-by-N) Column vector (N-by-1) Unoriented vector (N)	N	Scalar Column vector (M-by-1) Row vector (1-by-M) Matrix (M-by-N)	Scalar
Matrix (K-by-N)	K×N	Scalar Column vector (M-by-1) Row vector (1-by-M) Matrix (M-by-(K×N))	Scalar

When the Initial states is a scalar, the block initializes all filterstates to the same scalar value. To initialize all states to zero, enter0. When the Initial states is a vectoror a matrix, each vector or matrix element specifies a unique initial state for acorresponding delay element in a corresponding channel:

The vector length must equal the number of delay elements in thefilter, M = max(number of zeros, number ofpoles).
The matrix must have the same number of rows as the number of delayelements in the filter, M = max(number of zeros, number ofpoles). The matrix must also have one column for eachchannel of the input signal.

The following example shows the relationship between the initial filter output and theinitial input and state. Given an initial inputu₁, the first outputy₁ is related to the initial state[x₁,x₂] and initial input by asfollows:

$\begin{array}{l} y 1 = 4 x 1 \\ x 2 = 1 / 2 (u 1 - 3 x 1) \end{array}$

Examples

Designing a High Angle of Attack Pitch Mode ControlUse the Control System Toolbox™ and Simulink® Control Design™ to interact with Simulink to design a digital pitch control for the aircraft. In this example, we will design the controller to permit the aircraft to operate at a high angle of attack with minimal pilot workload.

Open Model

Ports

Input

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u — Input signal
scalar | vector | matrix

Input signal, specified as a scalar, vector, or matrix.

When you set the Inputprocessing parameter to Columns as channels(frame based), the block supports variable-size inputsignals, that is, you can change the frame size (number of rows) of thesignal during simulation but the number of channels (columns) mustremain constant. (since R2024a)

Data Types: single | double | int8 | int16 | int32 | fixed point

Num — Numerator coefficients
scalar | vector | matrix

Coefficients of the numerator polynomial specified as a vector or matrix in descendingpowers of z. Use a row vector to specify thecoefficients for a single numerator polynomial. Use a matrix to specifycoefficients for multiple filters to be applied to the same input. Eachmatrix row represents a set of filter taps. The order of the denominatormust be greater than or equal to the order of the numerator.

Dependencies

To enable this port, set Numerator Source toInput port.

Numerator and denominator coefficients must have the samecomplexity. They can have different word lengths and fractionlengths.

Data Types: single | double | int8 | int16 | int32 | fixed point

Den — Denominator coefficients
scalar | vector | matrix

Coefficients of the denominator polynomial specified as a vector in descending powers ofz. Use a row vector to specify the coefficientsfor a single denominator polynomial. Use a matrix to specifycoefficients for multiple filters to be applied to the same input. Eachmatrix row represents a set of filter taps. The order of the denominatormust be greater than or equal to the order of the numerator. The leadingdenominator coefficient cannot be 0.

Dependencies

To enable this port, set Denominator Sourceto Input port.

Numerator and denominator coefficients must have the samecomplexity. They can have different word lengths and fractionlengths.

Data Types: single | double | int8 | int16 | int32 | fixed point

External reset — External reset signal
scalar

External reset signal, specified as a scalar. When the specifiedtrigger event occurs, the block resets the states to their initial conditions.

Tip

The icon for this port changes based on the value of theExternal reset parameter.

Dependencies

To enable this port, set External reset toRising,Falling,Either,Level, or Levelhold.

Limitations

The reset signal must be a scalar of type single, double, Boolean, or integer.Fixed-point data types, except for ufix1, are notsupported.

Data Types: single | double | Boolean | int8 | int16 | int32 | fixed point

x0 — Initial states
scalar | vector | matrix

Initial states, specified as a scalar, vector, or matrix. For more information aboutspecifying states, see Specifying Initial States. States are complex wheneither the input or the coefficients are complex.

Dependencies

To enable this port, set Initial statesSource to Inputport.

Data Types: single | double | int8 | int16 | int32 | fixed point

Output

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Port_1 — Output signal
scalar | vector | matrix

Output signal specified as a scalar, vector, or matrix.

When you set Sample time to-1, sample time of the output signal is same as thesample time of the input signal u.

Data Types: single | double | int8 | int16 | int32 | fixed point

Parameters

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Main

Numerator Source — Source of numerator coefficients
`Dialog` (default) | `Input port`

Specify the source of the numerator coefficients asDialog or Inputport.

Programmatic Use

Block Parameter:NumeratorSource

Type: character vector

Values:'Dialog' | 'Input port'

Default:'Dialog'

Numerator Value — Numerator coefficients
`[1]` (default) | scalar | vector | matrix

Numerator coefficients of the discrete transfer function. To specify the coefficients,set the Source toDialog. Then, enter the coefficients inValue as descending powers ofz. Use a row vector to specify the coefficientsfor a single numerator polynomial. Use a matrix to specify coefficientsfor multiple filters to be applied to the same input. Each matrix rowrepresents a set of filter taps.

Dependencies

To enable this parameter, set the NumeratorSource to Dialog.

Programmatic Use

Block Parameter:Numerator

Type: character vector

Values: scalar | vector |matrix

Default:'[1]'

Denominator Source — Source of denominator coefficients
`Dialog` (default) | `Input port`

Specify the source of the denominator coefficients asDialog or Inputport.

Programmatic Use

Block Parameter:DenominatorSource

Type: character vector

Values:'Dialog' | 'Input port'

Default:'Dialog'

Denominator Value — Denominator coefficients
`[1 0.5]` (default) | scalar | vector | matrix

Denominator coefficients of the discrete transfer function. To specifythe coefficients, set the Source toDialog. Then, enter the coefficients inValue as descending powers ofz. Use a row vector to specify the coefficientsfor a single denominator polynomial. Use a matrix to specifycoefficients for multiple filters to be applied to the same input. Eachmatrix row represents a set of filter taps.

Dependencies

To enable this parameter, set the DenominatorSource to Dialog.

Programmatic Use

Block Parameter:Denominator

Type: character vector

Values: scalar | vector |matrix

Default:'[1 0.5]'

Initial states Source — Source of initial states
`Dialog` (default) | `Input port`

Specify the source of the initial states asDialog or Inputport.

Programmatic Use

Block Parameter:InitialStatesSource

Type: character vector

Values:'Dialog' | 'Input port'

Default:'Dialog'

Initial states Value — Initial filter states
`0` (default) | scalar | vector | matrix

Specify the initial filter states as a scalar, vector, or matrix. Tolearn how to specify initial states, see Specifying Initial States.

Dependencies

To enable this parameter, set Initial statesSource to Dialog.

Programmatic Use

Block Parameter:InitialStates

Type: character vector

Values: scalar | vector |matrix

Default:'0'

External reset — External state reset
`None` (default) | `Rising` | `Falling` | `Either` | `Level` | `Level hold`

Specify the trigger event to use to reset the states to the initial conditions.

Reset Mode	Behavior
`None`	No reset
`Rising`	Reset on a rising edge
`Falling`	Reset on a falling edge
`Either`	Reset on either a rising or falling edge
`Level`	Reset in either of these cases: When the reset signal is nonzero at the current time step When the reset signal value changes from nonzero at the previous time step to zero at the current time step
`Level hold`	Reset when the reset signal is nonzero at the current time step

Programmatic Use

Block Parameter: ExternalReset

Type: character vector

Default: 'None'

Input processing — Sample- or frame-based processing
`Elements as channels (samplebased)` (default) | `Columns as channels (frame based)`

Specify whether the block performs sample- or frame-basedprocessing.

Elements as channels (sample based)— Process each element of the input as an independentchannel.
Columns as channels (frame based)— Process each column of the input as an independentchannel.
Note
Frame-based processing requires a DSP System Toolbox license.
For more information, see Sample- and Frame-Based Concepts (DSP System Toolbox).

Programmatic Use

Block Parameter:InputProcessing

Type: character vector

Values:'Elements as channels (sample based)' | 'Columns aschannels (frame based)'

Default:'Elements as channels (samplebased)'

Optimize by skipping divide by leading denominator coefficient (a0) — Skip divide by a0
`off` (default) | `on`

Select when the leading denominator coefficient,a₀, equals 1. Thisparameter optimizes your code.

When you select this check box, the block does not perform adivide-by-a₀ either insimulation or in the generated code. An error occurs if you specify thedenominator coefficients in the block dialog box anda₀ ≠ 1.

When you clear this check box, the block is fully tunable duringsimulation, and performs adivide-by-a₀ in bothsimulation and code generation.

Programmatic Use

Block Parameter:a0EqualsOne

Type: character vector

Values:'off' | 'on'

Default:'off'

Sample time (-1 for inherited) — Interval between samples
`-1` (default) | scalar | vector

Specify the time interval between samples. To inherit the sample time, set this parameter to -1. For more information, see Specify Sample Time.

Dependencies

This parameter is visible only if you set it to a value other than -1. To learn more, see Blocks for Which Sample Time Is Not Recommended.

Programmatic Use

Block Parameter: SampleTime

Type: string scalar or character vector

Default: "-1"

Data Types

State — State data type
`Inherit: Same as input` (default) | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Specify the state data type. You can set it to:

A rule that inherits a data type, for example,Inherit: Same as input
A built-in integer, for example,int8
A data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Programmatic Use

Block Parameter:StateDataTypeStr

Type: character vector

Values:'Inherit: Same as input' | 'int8' | 'int16' | 'int32' |'int64' | 'fixdt(1,16,0)' | '<data typeexpression>'

Default:'Inherit: Same as input'

Numerator coefficients — Numerator coefficient data type
`Inherit: Inherit via internalrule` (default) | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16)` | `fixdt(1,16,0)` | `<data type expression>`

Specify the numerator coefficient data type. You can set it to:

A rule that inherits a data type, for example,Inherit: Inherit via internalrule
A built-in integer, for example,int8
A data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Programmatic Use

Block Parameter: NumCoefDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal rule' | 'int8' | 'int16'| 'int32' | 'int64' | 'fixdt(1,16)' | 'fixdt(1,16,0)' |'<data type expression>'

Default:'Inherit: Inherit via internal rule'

Numerator coefficient minimum — Minimum value of numerator coefficients
`[]` (default) | scalar

Specify the minimum value that a numerator coefficient can have. Thedefault value is [] (unspecified). Simulink^® software uses this value to perform:

Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixed-point data types
See Also
Handle transfer of data between blocks operating at different rates

Programmatic Use

Block Parameter:NumCoefMin

Type: character vector

Values: scalar

Default:'[]'

Numerator coefficient maximum — Maximum value of numerator coefficients
`[]` (default) | scalar

Specify the maximum value that a numerator coefficient can have. Thedefault value is [] (unspecified). Simulink software uses this value to perform:

Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixed-point data types

Programmatic Use

Block Parameter:NumCoefMax

Type: character vector

Values: scalar

Default:'[]'

Numerator product output — Numerator product output data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Specify the product output data type for the numerator coefficients.You can set it to:

A rule that inherits a data type, for example,Inherit: Inherit via internalrule
A built-in data type, for example,int8
A data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Programmatic Use

Block Parameter:NumProductDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal rule' | 'Inherit: Sameas input' | 'int8' | 'int16' | 'int32' | 'int64' |'fixdt(1,16,0)' | '<data typeexpression>'

Default:'Inherit: Inherit via internal rule'

Numerator accumulator — Numerator accumulator data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `Inherit: Same as product output` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Specify the accumulator data type for the numerator coefficients. Youcan set it to:

A rule that inherits a data type, for example,Inherit: Inherit via internalrule
A built-in data type, for example,int8
A data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Programmatic Use

Block Parameter:NumAccumDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal rule' | 'Inherit: Sameas input' | 'Inherit: Same as product output' | 'int8' |'int16' | 'int32' | 'int64' | 'fixdt(1,16,0)' | '<datatype expression>'

Default:'Inherit: Inherit via internal rule'

Denominator coefficients — Denominator coefficient data type
`Inherit: Inherit via internalrule` (default) | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16)` | `fixdt(1,16,0)` | `<data type expression>`

Specify the denominator coefficient data type. You can set itto:

A rule that inherits a data type, for example,Inherit: Inherit via internalrule
A built-in integer, for example,int8
A data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Programmatic Use

Block Parameter:DenCoefDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal rule' | 'int8' | 'int16'| 'int32' | 'int64' | 'fixdt(1,16)' | 'fixdt(1,16,0)' |'<data type expression>'

Default:'Inherit: Inherit via internal rule'

Denominator coefficient minimum — Minimum value of denominator coefficients
`[]` (default) | scalar

Specify the minimum value that a denominator coefficient can have. Thedefault value is [] (unspecified). Simulink software uses this value to perform:

Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixed-point data types

Programmatic Use

Block Parameter:DenCoefMin

Type: character vector

Values: scalar

Default:'[]'

Denominator coefficient maximum — Maximum value of denominator coefficients
`[]` (default) | scalar

Specify the maximum value that a denominator coefficient can have. Thedefault value is [] (unspecified). Simulink software uses this value to perform:

Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixed-point data types

Programmatic Use

Block Parameter:DenCoefMax

Type: character vector

Values: scalar

Default:'[]'

Denominator product output — Denominator product output data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Specify the product output data type for the denominator coefficients.You can set it to:

A rule that inherits a data type, for example,Inherit: Inherit via internalrule
A built-in data type, for example,int8
A data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Programmatic Use

Block Parameter:DenProductDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal rule' | 'Inherit: Sameas input' | 'int8' | 'int16' | 'int32' | 'int64' |'fixdt(1,16,0)' | '<data typeexpression>'

Default:'Inherit: Inherit via internal rule'

Denominator accumulator — Denominator accumulator data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `Inherit: Same as product output` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Specify the accumulator data type for the denominator coefficients.You can set it to:

A rule that inherits a data type, for example,Inherit: Inherit via internalrule
A built-in data type, for example,int8
A data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Programmatic Use

Block Parameter:DenAccumDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal rule' | 'Inherit: Sameas input' | 'Inherit: Same as product output' | 'int8' |'int16' | 'int32' | 'int64' | 'fixdt(1,16,0)' | '<datatype expression>'

Default:'Inherit: Inherit via internal rule'

Output — Output data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16)` | `fixdt(1,16,0)` | `<data type expression>`

Specify the output data type. You can set it to:

A rule that inherits a data type, for example,Inherit: Inherit via internalrule
A built-in data type, for example,int8
A data type object, for example, aSimulink.NumericType object
An expression that evaluates to a data type, for example,fixdt(1,16,0)

The Data Type Assistant helps you set dataattributes. To use the Data Type Assistant, click . For more information, see Specify Data Types Using Data Type Assistant.

Programmatic Use

Block Parameter:OutDataTypeStr

Type: character vector

Values:

'Inherit: Inherit via internal rule' | 'Inherit: Sameas input' | 'int8' | 'int16' | 'int32' | 'int64' |'fixdt(1,16)' | 'fixdt(1,16,0)' | '<data typeexpression>'

Default:'Inherit: Inherit via internal rule'

Output minimum — Minimum value of output
`[]` (default) | scalar

Specify the minimum value that the block can output. The default valueis [] (unspecified). Simulink uses this value to perform:

Simulation range checking (see Specify Signal Ranges)
Automatic scaling of fixed-point data types

Programmatic Use

Block Parameter:OutMin

Type: character vector

Values: scalar

Default:'[]'

Output maximum — Maximum value of output
`[]` (default) | scalar

Specify the maximum value that the block can output. The default valueis [] (unspecified). Simulink uses this value to perform:

Simulation range checking (see Specify Signal Ranges)
Automatic scaling of fixed-point data types

Programmatic Use

Block Parameter:OutMax

Type: character vector

Values: scalar

Default:'[]'

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 on this block. For more information, see Lock the Output Data Type Setting (Fixed-Point Designer).

Programmatic Use

Block Parameter: LockScale

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Integer rounding mode — Rounding mode for fixed-point operations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Specify the rounding mode for fixed-point operations. For more information, see Rounding (Fixed-Point Designer).

Block parameters always round to the nearest representable value. To control the rounding of a block parameter, enter an expression using a MATLAB^® rounding function into the mask field.

Programmatic Use

Block Parameter: RndMeth

Type: character vector

Default: 'Floor'

Saturate on integer overflow — Method of overflow action
`off` (default) | `on`

Specify whether overflows saturate or wrap.

Action Rationale Impact on Overflows Example

Action	Rationale	Impact on Overflows	Example
Select this check box (`on`).	Your model has possible overflow, and you want explicit saturation protection in the generated code.	Overflows saturate to either the minimum or maximum value that the data type can represent.	The maximum value that the `int8` (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box selected, the block output saturates at 127. Similarly, the block output saturates at a minimum output value of -128.
Do not select this check box (`off`).	You want to optimize efficiency of your generated code. You want to avoid overspecifying how a block handles out-of-range signals. For more information, see Troubleshoot Signal Range Errors.	Overflows wrap to the appropriate value that is representable by the data type.	The maximum value that the `int8` (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box cleared, the software interprets the overflow-causing value as `int8`, which can produce an unintended result. For example, a block result of 130 (binary 1000 0010) expressed as `int8`, is -126.

Select this check box (on).

Your model has possible overflow, and you want explicit saturation protection in the generated code.

Overflows saturate to either the minimum or maximum value that the data type can represent.

The maximum value that the int8 (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box selected, the block output saturates at 127. Similarly, the block output saturates at a minimum output value of -128.

Do not select this check box (off).

You want to optimize efficiency of your generated code.

You want to avoid overspecifying how a block handles out-of-range signals. For more information, see Troubleshoot Signal Range Errors.

Overflows wrap to the appropriate value that is representable by the data type.

The maximum value that the int8 (signed, 8-bit integer) data type can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer. With the check box cleared, the software interprets the overflow-causing value as int8, which can produce an unintended result. For example, a block result of 130 (binary 1000 0010) expressed as int8, is -126.

When you select this check box, saturation applies to every internal operation on the block, not just the output, or result. Usually, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

Programmatic Use

Block Parameter: SaturateOnIntegerOverflow

Type: character vector

Values: 'off' | 'on'

Default: 'off'

State Attributes

State name — Unique name for block state
`''` (default) | alphanumeric string

Use this parameter to assign a unique name to the block state. The default is ' '. When this field is blank, no name is assigned. When using this parameter, remember these considerations:

A valid identifier starts with an alphabetic or underscore character, followed by alphanumeric or underscore characters.
The state name applies only to the selected block.

This parameter enables State name must resolve to Simulink signal object when you click Apply.

For more information, see C Data Code Interface Configuration for Model Interface Elements (Simulink Coder).

Programmatic Use

Block Parameter: StateName

Type: character vector

Values: unique name

Default: ''

State name must resolve to Simulink signal object — Require state name resolve to a signal object
`off` (default) | `on`

Select this check box to require that the state name resolves to a Simulink signal object.

Dependencies

To enable this parameter, specify a value for State name. This parameter appears only if you set the model configuration parameter Signal resolution to a value other than None.

Programmatic Use

Block Parameter: StateMustResolveToSignalObject

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Block Characteristics

Data Types	`double` \| `fixed point^a` \| `integer^a` \| `single`
Direct Feedthrough	`no`
Multidimensional Signals	`no`
Variable-Size Signals	`yes`
Zero-Crossing Detection	`no`
^aThis block only supports signed fixed-point data types.

Extended Capabilities

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

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDLimplementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

General
ConstMultiplierOptimization	Canonical signed digit (CSD) or factored CSD optimization. Thedefault is `none`. See also ConstMultiplierOptimization (HDL Coder).
ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is `0`. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see OutputPipeline (HDL Coder).

Native Floating Point
HandleDenormals	Specify whether you want HDL Coder to insert additional logic to handle denormal numbers in your design. Denormal numbers are numbers that have magnitudes less than the smallest floating-point number that can be represented without leading zeros in the mantissa. The default is `inherit`. See also HandleDenormals (HDL Coder).
LatencyStrategy	Specify whether to map the blocks in your design to `inherit`, `Max`, `Min`, or `Zero` for the floating-point operator. The default is `inherit`. See also LatencyStrategy (HDL Coder).
MantissaMultiplyStrategy	Specify how to implement the mantissa multiplication operation during code generation. By using different settings, you can control the DSP usage on the target FPGA device. The default is `inherit`. See also MantissaMultiplyStrategy (HDL Coder).

Restrictions

Double data types are not supported for this block. Use singledata types instead.
Frame, matrix, and vector input data types are notsupported.
The leading denominator coefficient (a0) must be 1 or -1.
Setting output data type as Inherit: Inherit via internalrule is not supported.

The Discrete Transfer Fcn block is excluded from the following optimizations:

Resource sharing
Distributed pipelining

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

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

This block only supports signed fixed-point data types.

Version History

Introduced before R2006a

expand all

R2024a: The Discrete Transfer Fcn block supports variable-size inputsignals

The Discrete Transfer Fcn block supports variable-size inputsignals when you set the Input processing parameter toColumns as channels (frame based).

When the input is a variable-size signal, you can change the frame size (number ofrows) of the signal during simulation but the number of channels (columns) mustremain constant.

R2023b: Conditional display of the Sample time parameter

The Discrete Transfer Fcn block no longer displays the Sampletime parameter in the block parameters dialog box by default. Theparameter is visible only if you set the sample time to a value other the defaultvalue (-1) at the command line or in an existing model. For moreinformation, see Blocks for Which Sample Time Is Not Recommended.

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Implement discrete transfer function - Simulink (2024)

Description

Specifying Initial States

Examples

Ports

Input

u — Input signalscalar | vector | matrix

Num — Numerator coefficients scalar | vector | matrix

Dependencies

Den — Denominator coefficients scalar | vector | matrix

Dependencies

External reset — External reset signal scalar

Dependencies

Limitations

x0 — Initial states scalar | vector | matrix

Dependencies

Output

Port_1 — Output signalscalar | vector | matrix

Parameters

Main

Numerator Source — Source of numerator coefficientsDialog (default) | Input port

Programmatic Use

Numerator Value — Numerator coefficients [1] (default) | scalar | vector | matrix

Dependencies

Programmatic Use

Denominator Source — Source of denominator coefficients Dialog (default) | Input port

Programmatic Use

Denominator Value — Denominator coefficients [1 0.5] (default) | scalar | vector | matrix

Dependencies

Programmatic Use

Initial states Source — Source of initial states Dialog (default) | Input port

Programmatic Use

Initial states Value — Initial filter states 0 (default) | scalar | vector | matrix

Dependencies

Programmatic Use

External reset — External state reset None (default) | Rising | Falling | Either | Level | Level hold

Programmatic Use

Input processing — Sample- or frame-based processing Elements as channels (samplebased) (default) | Columns as channels (frame based)

Programmatic Use

Optimize by skipping divide by leading denominator coefficient (a0) — Skip divide by a0 off (default) | on

Programmatic Use

Sample time (-1 for inherited) — Interval between samples -1 (default) | scalar | vector

Dependencies

Programmatic Use

Data Types

State — State data typeInherit: Same as input (default) | int8 | int16 | int32 | int64 | fixdt(1,16,0) | <data type expression>

Programmatic Use

Numerator coefficients — Numerator coefficient data type Inherit: Inherit via internalrule (default) | int8 | int16 | int32 | int64 | fixdt(1,16) | fixdt(1,16,0) | <data type expression>

Programmatic Use

Numerator coefficient minimum — Minimum value of numerator coefficients [] (default) | scalar

Programmatic Use

Numerator coefficient maximum — Maximum value of numerator coefficients [] (default) | scalar

Programmatic Use

Numerator product output — Numerator product output data type Inherit: Inherit via internalrule (default) | Inherit: Same as input | int8 | int16 | int32 | int64 | fixdt(1,16,0) | <data type expression>

Programmatic Use

Numerator accumulator — Numerator accumulator data type Inherit: Inherit via internalrule (default) | Inherit: Same as input | Inherit: Same as product output | int8 | int16 | int32 | int64 | fixdt(1,16,0) | <data type expression>

Programmatic Use

Denominator coefficients — Denominator coefficient data type Inherit: Inherit via internalrule (default) | int8 | int16 | int32 | int64 | fixdt(1,16) | fixdt(1,16,0) | <data type expression>

Programmatic Use

Denominator coefficient minimum — Minimum value of denominator coefficients [] (default) | scalar

Programmatic Use

Denominator coefficient maximum — Maximum value of denominator coefficients [] (default) | scalar

Programmatic Use

Denominator product output — Denominator product output data type Inherit: Inherit via internalrule (default) | Inherit: Same as input | int8 | int16 | int32 | int64 | fixdt(1,16,0) | <data type expression>

Programmatic Use

Denominator accumulator — Denominator accumulator data type Inherit: Inherit via internalrule (default) | Inherit: Same as input | Inherit: Same as product output | int8 | int16 | int32 | int64 | fixdt(1,16,0) | <data type expression>

Programmatic Use

Output — Output data type Inherit: Inherit via internalrule (default) | Inherit: Same as input | int8 | int16 | int32 | int64 | fixdt(1,16) | fixdt(1,16,0) | <data type expression>

Programmatic Use

Output minimum — Minimum value of output [] (default) | scalar

Programmatic Use

Output maximum — Maximum value of output [] (default) | scalar

Programmatic Use

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

Programmatic Use

Integer rounding mode — Rounding mode for fixed-point operationsFloor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Programmatic Use

Saturate on integer overflow — Method of overflow action off (default) | on

Programmatic Use

State Attributes

u — Input signal
scalar | vector | matrix

Num — Numerator coefficients
scalar | vector | matrix

Den — Denominator coefficients
scalar | vector | matrix

External reset — External reset signal
scalar

x0 — Initial states
scalar | vector | matrix

Port_1 — Output signal
scalar | vector | matrix

Numerator Source — Source of numerator coefficients
`Dialog` (default) | `Input port`

Numerator Value — Numerator coefficients
`[1]` (default) | scalar | vector | matrix

Denominator Source — Source of denominator coefficients
`Dialog` (default) | `Input port`

Denominator Value — Denominator coefficients
`[1 0.5]` (default) | scalar | vector | matrix

Initial states Source — Source of initial states
`Dialog` (default) | `Input port`

Initial states Value — Initial filter states
`0` (default) | scalar | vector | matrix

External reset — External state reset
`None` (default) | `Rising` | `Falling` | `Either` | `Level` | `Level hold`

Input processing — Sample- or frame-based processing
`Elements as channels (samplebased)` (default) | `Columns as channels (frame based)`

Optimize by skipping divide by leading denominator coefficient (a0) — Skip divide by a0
`off` (default) | `on`

Sample time (-1 for inherited) — Interval between samples
`-1` (default) | scalar | vector

State — State data type
`Inherit: Same as input` (default) | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Numerator coefficients — Numerator coefficient data type
`Inherit: Inherit via internalrule` (default) | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16)` | `fixdt(1,16,0)` | `<data type expression>`

Numerator coefficient minimum — Minimum value of numerator coefficients
`[]` (default) | scalar

Numerator coefficient maximum — Maximum value of numerator coefficients
`[]` (default) | scalar

Numerator product output — Numerator product output data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Numerator accumulator — Numerator accumulator data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `Inherit: Same as product output` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Denominator coefficients — Denominator coefficient data type
`Inherit: Inherit via internalrule` (default) | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16)` | `fixdt(1,16,0)` | `<data type expression>`

Denominator coefficient minimum — Minimum value of denominator coefficients
`[]` (default) | scalar

Denominator coefficient maximum — Maximum value of denominator coefficients
`[]` (default) | scalar

Denominator product output — Denominator product output data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Denominator accumulator — Denominator accumulator data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `Inherit: Same as product output` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16,0)` | `<data type expression>`

Output — Output data type
`Inherit: Inherit via internalrule` (default) | `Inherit: Same as input` | `int8` | `int16` | `int32` | `int64` | `fixdt(1,16)` | `fixdt(1,16,0)` | `<data type expression>`

Output minimum — Minimum value of output
`[]` (default) | scalar

Output maximum — Maximum value of output
`[]` (default) | scalar

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

Integer rounding mode — Rounding mode for fixed-point operations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Saturate on integer overflow — Method of overflow action
`off` (default) | `on`

State name — Unique name for block state
`''` (default) | alphanumeric string

State name must resolve to Simulink signal object — Require state name resolve to a signal object
`off` (default) | `on`

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

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

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