# Discrete Transfer Fcn

Implement discrete transfer function

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

## Description

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

`$H\left(z\right)=\frac{num\left(z\right)}{den\left(z\right)}=\frac{nu{m}_{0}{z}^{m}+nu{m}_{1}{z}^{m-1}+...+nu{m}_{m}}{de{n}_{0}{z}^{n}+de{n}_{1}{z}^{n-1}+...+de{n}_{n}}$`

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

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

The Discrete Transfer Fcn block applies the z-transform transfer function to each independent channel of the input. The Input processing parameter allows you to specify whether the block treats each column of the input as an individual channel (frame-based processing) or each element of the input as an individual channel (sample-based processing). To perform frame-based processing, 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 blocks that are used in the filter digram implementing the discrete transfer function.

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

Frame-Based Processing

Input Number of ChannelsValid 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

InputNumber of ChannelsValid 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 filter states to the same scalar value. To initialize all states to zero, enter `0`. When the Initial states is a vector or a matrix, each vector or matrix element specifies a unique initial state for a corresponding delay element in a corresponding channel:

• The vector length must equal the number of delay elements in the filter, ```M = max(number of zeros, number of poles)```.

• The matrix must have the same number of rows as the number of delay elements in the filter, ```M = max(number of zeros, number of poles)```. The matrix must also have one column for each channel of the input signal.

The following example shows the relationship between the initial filter output and the initial input and state. Given an initial input u1, the first output y1 is related to the initial state [x1, x2] and initial input by as follows:

`$\begin{array}{l}y1=4x1\\ x2=1/2\left(u1-3x1\right)\end{array}$`

## Ports

### Input

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

When you set the Input processing parameter to ```Columns as channels (frame based)```, the block supports variable-size input signals, that is, you can change the frame size (number of rows) of the signal during simulation but the number of channels (columns) must remain constant. (since R2024a)

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

Coefficients of the numerator polynomial specified as a vector or matrix in descending powers of z. Use a row vector to specify the coefficients for a single numerator polynomial. Use a matrix to specify coefficients for multiple filters to be applied to the same input. Each matrix row represents a set of filter taps. The order of the denominator must be greater than or equal to the order of the numerator.

#### Dependencies

To enable this port, set Numerator Source to `Input port`.

Numerator and denominator coefficients must have the same complexity. They can have different word lengths and fraction lengths.

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

Coefficients of the denominator polynomial specified as a vector in descending powers of z. Use a row vector to specify the coefficients for a single denominator polynomial. Use a matrix to specify coefficients for multiple filters to be applied to the same input. Each matrix row represents a set of filter taps. The order of the denominator must be greater than or equal to the order of the numerator. The leading denominator coefficient cannot be `0`.

#### Dependencies

To enable this port, set Denominator Source to `Input port`.

Numerator and denominator coefficients must have the same complexity. They can have different word lengths and fraction lengths.

To set Denominator Source to `Input port`, you must select the Optimize by skipping divide by leading denominator coefficient (a0) parameter. The block ignores the leading denominator coefficient value a0 and replaces it with a 1.

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

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

Tip

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

#### Dependencies

To enable this port, set External reset to `Rising`, `Falling`, `Either`, `Level`, or ```Level hold```.

#### Limitations

The reset signal must be a scalar of type single, double, Boolean, or integer. Fixed-point data types, except for `ufix1`, are not supported.

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

Initial states, specified as a scalar, vector, or matrix. For more information about specifying states, see Specifying Initial States. States are complex when either the input or the coefficients are complex.

#### Dependencies

To enable this port, set Initial states Source to ```Input port```.

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

### Output

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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 the sample time of the input signal u.

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

## Parameters

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### Main

Specify the source of the numerator coefficients as `Dialog` or ```Input port```.

#### Programmatic Use

 Block Parameter: `NumeratorSource` Type: character vector Values: `'Dialog' | 'Input port'` Default: `'Dialog'`

Numerator coefficients of the discrete transfer function. To specify the coefficients, set the Source to `Dialog`. Then, enter the coefficients in Value as descending powers of z. Use a row vector to specify the coefficients for a single numerator polynomial. Use a matrix to specify coefficients for multiple filters to be applied to the same input. Each matrix row represents a set of filter taps.

#### Dependencies

To enable this parameter, set the Numerator Source to `Dialog`.

#### Programmatic Use

 Block Parameter: `Numerator` Type: character vector Values: scalar | vector | matrix Default: `'[1]'`

Specify the source of the denominator coefficients as `Dialog` or ```Input port```.

To set Denominator Source to ```Input port```, you must select the Optimize by skipping divide by leading denominator coefficient (a0) parameter.

#### Programmatic Use

 Block Parameter: `DenominatorSource` Type: character vector Values: `'Dialog' | 'Input port'` Default: `'Dialog'`

Denominator coefficients of the discrete transfer function. To specify the coefficients, set the Source to `Dialog`. Then, enter the coefficients in Value as descending powers of z. Use a row vector to specify the coefficients for a single denominator polynomial. Use a matrix to specify coefficients for multiple filters to be applied to the same input. Each matrix row represents a set of filter taps.

When you select the Optimize by skipping divide by leading denominator coefficient (a0) parameter, an error occurs if you specify the denominator coefficients in the block dialog box and a0 ≠ 1.

#### Dependencies

To enable this parameter, set the Denominator Source to `Dialog`.

#### Programmatic Use

 Block Parameter: `Denominator` Type: character vector Values: scalar | vector | matrix Default: `'[1 0.5]'`

Specify the source of the initial states as `Dialog` or ```Input port```.

#### Programmatic Use

 Block Parameter: `InitialStatesSource` Type: character vector Values: `'Dialog' | 'Input port'` Default: `'Dialog'`

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

#### Dependencies

To enable this parameter, set Initial states Source to `Dialog`.

#### Programmatic Use

 Block Parameter: `InitialStates` Type: character vector Values: scalar | vector | matrix Default: `'0'`

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

Reset ModeBehavior
`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 Values: `'None'` | `'Rising'` | `'Falling'` | `'Either'` | `'Level'` | ```'Level hold'``` Default: `'None'`

Specify whether the block performs sample- or frame-based processing.

• `Elements as channels (sample based)` — Process each element of the input as an independent channel.

• `Columns as channels (frame based)` — Process each column of the input as an independent channel.

Note

Frame-based processing requires a DSP System Toolbox license.

#### Programmatic Use

 Block Parameter: `InputProcessing` Type: character vector Values: ```'Elements as channels (sample based)' | 'Columns as channels (frame based)'``` Default: ```'Elements as channels (sample based)'```

When you select this check box, the block does not perform a divide-by-a0 either in simulation or in the generated code. This parameter optimizes your code. An error occurs if you specify the denominator coefficients in the block dialog box and a0 ≠ 1.

If you specify the denominator coefficients from the input port Den, you must select the Optimize by skipping divide by leading denominator coefficient (a0) parameter. When you select this checkbox, the block ignores the leading denominator coefficient a0 and replaces it with a 1.

When you clear this check box, the block is fully tunable during simulation. It performs a divide-by-a0 in both simulation and code generation.

#### Programmatic Use

 Block Parameter: `a0EqualsOne` Type: character vector Values: `'off' | 'on'` Default: `'off'`

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

To set the block parameter value programmatically, use the `set_param` function.

 Parameter: `SampleTime` Values: `"-1"` (default) | scalar or vector in quotes

Click this button to open the Filter Visualization Tool (`fvtool` (DSP System Toolbox)) and display the filter response of the filter defined in the block dialog box.

#### Dependencies

To enable this parameter, set the Numerator Source and Denominator Source parameters to `Dialog`.

This parameter appears only if you have a valid DSP System Toolbox license.

### Data Types

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, a `Simulink.NumericType` object

• An expression that evaluates to a data type, for example, `fixdt(1,16,0)`

The Data Type Assistant helps you set data attributes. 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)' | ''``` Default: `'Inherit: Same as input'`

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

• A rule that inherits a data type, for example, ```Inherit: Inherit via internal rule```

• A built-in integer, for example, `int8`

• A data type object, for example, a `Simulink.NumericType` object

• An expression that evaluates to a data type, for example, `fixdt(1,16,0)`

The Data Type Assistant helps you set data attributes. 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)' | ''``` Default: `'Inherit: Inherit via internal rule'`

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

#### Programmatic Use

 Block Parameter: `NumCoefMin` Type: character vector Values: scalar Default: `'[]'`

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

#### Programmatic Use

 Block Parameter: `NumCoefMax` Type: character vector Values: scalar Default: `'[]'`

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 internal rule```

• A built-in data type, for example, `int8`

• A data type object, for example, a `Simulink.NumericType` object

• An expression that evaluates to a data type, for example, `fixdt(1,16,0)`

The Data Type Assistant helps you set data attributes. 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: Same as input' | 'int8' | 'int16' | 'int32' | 'int64' | 'fixdt(1,16,0)' | ''``` Default: `'Inherit: Inherit via internal rule'`

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

• A rule that inherits a data type, for example, ```Inherit: Inherit via internal rule```

• A built-in data type, for example, `int8`

• A data type object, for example, a `Simulink.NumericType` object

• An expression that evaluates to a data type, for example, `fixdt(1,16,0)`

The Data Type Assistant helps you set data attributes. 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: Same as input' | 'Inherit: Same as product output' | 'int8' | 'int16' | 'int32' | 'int64' | 'fixdt(1,16,0)' | ''``` Default: `'Inherit: Inherit via internal rule'`

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

• A rule that inherits a data type, for example, ```Inherit: Inherit via internal rule```

• A built-in integer, for example, `int8`

• A data type object, for example, a `Simulink.NumericType` object

• An expression that evaluates to a data type, for example, `fixdt(1,16,0)`

The Data Type Assistant helps you set data attributes. 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)' | ''``` Default: `'Inherit: Inherit via internal rule'`

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

#### Programmatic Use

 Block Parameter: `DenCoefMin` Type: character vector Values: scalar Default: `'[]'`

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

#### Programmatic Use

 Block Parameter: `DenCoefMax` Type: character vector Values: scalar Default: `'[]'`

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 internal rule```

• A built-in data type, for example, `int8`

• A data type object, for example, a `Simulink.NumericType` object

• An expression that evaluates to a data type, for example, `fixdt(1,16,0)`

The Data Type Assistant helps you set data attributes. 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: Same as input' | 'int8' | 'int16' | 'int32' | 'int64' | 'fixdt(1,16,0)' | ''``` Default: `'Inherit: Inherit via internal rule'`

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 internal rule```

• A built-in data type, for example, `int8`

• A data type object, for example, a `Simulink.NumericType` object

• An expression that evaluates to a data type, for example, `fixdt(1,16,0)`

The Data Type Assistant helps you set data attributes. 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: Same as input' | 'Inherit: Same as product output' | 'int8' | 'int16' | 'int32' | 'int64' | 'fixdt(1,16,0)' | ''``` Default: `'Inherit: Inherit via internal rule'`

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

• A rule that inherits a data type, for example, ```Inherit: Inherit via internal rule```

• A built-in data type, for example, `int8`

• A data type object, for example, a `Simulink.NumericType` object

• An expression that evaluates to a data type, for example, `fixdt(1,16,0)`

The Data Type Assistant helps you set data attributes. 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: Same as input' | 'int8' | 'int16' | 'int32' | 'int64' | 'fixdt(1,16)' | 'fixdt(1,16,0)' | ''``` Default: `'Inherit: Inherit via internal rule'`

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

#### Programmatic Use

 Block Parameter: `OutMin` Type: character vector Values: scalar Default: `'[]'`

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

#### Programmatic Use

 Block Parameter: `OutMax` Type: character vector Values: scalar Default: `'[]'`

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'`

Specify the rounding mode for fixed-point operations. For more information, see Rounding Modes (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

To set the block parameter value programmatically, use the `set_param` function.

 Parameter: `RndMeth` Values: `'Floor'` (default) | `'Ceiling'` | `'Convergent'` | `'Nearest'` | `'Round'` | `'Simplest'` | `'Zero'`

Specify whether overflows saturate or wrap.

• `on` — Overflows saturate to either the minimum or maximum value that the data type can represent.

• `off` — Overflows wrap to the appropriate value that the data type can represent.

For example, the maximum value that the signed 8-bit integer `int8` can represent is 127. Any block operation result greater than this maximum value causes overflow of the 8-bit integer.

• With this parameter selected, the block output saturates at 127. Similarly, the block output saturates at a minimum output value of -128.

• With this parameter 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.

#### Tips

• Consider selecting this parameter when your model has a possible overflow and you want explicit saturation protection in the generated code.

• Consider clearing this parameter when you want to optimize efficiency of your generated code. Clearing this parameter also helps you to avoid overspecifying how a block handles out-of-range signals. For more information, see Troubleshoot Signal Range Errors.

• When you select this parameter, saturation applies to every internal operation on the block, not just the output or result.

• In general, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

#### Programmatic Use

To set the block parameter value programmatically, use the `set_param` function.

 Parameter: `SaturateOnIntegerOverflow` Values: `'off'` (default) | `'on'`

### State Attributes

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.

#### Programmatic Use

 Block Parameter: `StateName` Type: character vector Values: unique name Default: `''`

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 pointa` | `integera` | `single` Direct Feedthrough `no` Multidimensional Signals `no` Variable-Size Signals `yes` Zero-Crossing Detection `no` a This block only supports signed fixed-point data types.

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## Version History

Introduced before R2006a

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