Discrete Filter

Model Infinite Impulse Response (IIR) filters

Libraries:
Simulink / Discrete
DSP System Toolbox / Filtering / Filter Implementations

Description

The Discrete Filter block independently filters each channel of the input signal with the specified digital IIR filter. You can specify the filter structure as Direct form I, Direct form I transposed, Direct form II, or Direct form II transposed. The block implements static filters with fixed coefficients. You can tune the coefficients of these static filters.

This block filters each channel of the input signal independently over time. The Input processing parameter allows you to specify how the block treats each element of the input. You can specify treating input elements as an independent channel (sample-based processing), or treating each column of the input as an independent channel (frame-based processing). To perform frame-based processing, you must have a DSP System Toolbox™ license.

The output dimensions equal the input dimensions, except when you specify a matrix of filter taps for the Numerator coefficients parameter. When you do so, the output dimensions depend on the number of different sets of filter taps you specify.

Use the Numerator coefficients parameter to specify the coefficients of the discrete filter numerator polynomial. Use the Denominator coefficients parameter to specify the coefficients of the denominator polynomial of the function. The Denominator coefficients parameter must be a vector of coefficients.

Specify the coefficients of the numerator and denominator polynomials in ascending powers of z^-1. The Discrete Filter block lets you use polynomials in z^-1 (the delay operator) to represent a discrete system. Signal processing engineers typically use this method. Conversely, the Discrete Transfer Fcn block lets you use polynomials in z to represent a discrete system. Control engineers typically use this method. When the numerator and denominator polynomials have the same length, the two methods are identical.

Specifying Initial States

In Dialog parameters and Input port(s) modes, the block initializes the internal filter states to zero by default, which is equivalent to assuming past inputs and outputs are zero. You can optionally use the Initial states parameter to specify nonzero initial states for the filter delays.

To determine the number of initial state values you must specify, and how to specify them, see the following table on valid initial states and Number of Delay Elements (Filter States). The Initial states parameter can take one of four forms as described in the following table.

Valid Initial States

Initial state	Examples	Description
Scalar	`5` Each delay element for each channel is set to `5`.	The block initializes all delay elements in the filter to the scalar value.
Vector (for applying the same delay elements to each channel)	For a filter with two delay elements: [d₁d₂] The delay elements for all channels are d1 and d2.	Each vector element specifies a unique initial condition for a corresponding delay element. The block applies the same vector of initial conditions to each channel of the input signal. The vector length must equal the number of delay elements in the filter (specified in the table Number of Delay Elements (Filter States)).
Vector or matrix (for applying different delay elements to each channel)	For a three-channel input signal and a filter with two delay elements: [d₁d₂D₁D₂d₁d₂] or $[\begin{array}{l} d_{1} & D_{1} & d_{1} \\ d_{2} & D_{2} & d_{2} \end{array}]$ The delay elements for channel 1 are d₁ and d₂. The delay elements for channel 2 are D₁ and D₂. The delay elements for channel 3 are d₁and d₂.	Each vector or matrix element specifies a unique initial condition for a corresponding delay element in a corresponding channel: The vector length must be equal to the product of the number of input channels and the number of delay elements in the filter (specified in the table Number of Delay Elements (Filter States)). The matrix must have the same number of rows as the number of delay elements in the filter (specified in the table Number of Delay Elements (Filter States)), and must have one column for each channel of the input signal.
Empty matrix	`[ ]` Each delay element for each channel is set to `0`.	The empty matrix, `[]`, is equivalent to setting the Initial conditions parameter to the scalar value `0`.

The number of delay elements (filter states) per input channel depends on the filter structure, as indicated in the following table.

Number of Delay Elements (Filter States)

Filter Structure	Number of Delay Elements Per Channel
`Direct form I Direct form I transposed`	`number of zeros - 1` `number of poles - 1`
`Direct form II Direct form II transposed`	`max(number of zeros, number of poles)-1`

The following tables describe the valid initial states for different sizes of input and different number of channels depending on whether you set the Input processing parameter to frame based or sample based.

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)
Unoriented 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. Enter 0 to initialize all states to zero. When the Initial states is a vector or a matrix, each vector or matrix element specifies a unique initial state. This unique state corresponds to a 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 relationship between the initial filter output y₁, the initial input u₁, and the initial state [x₁, x₂] is given by the following equation.

$y_{1} = b_{1} [\frac{(u_{1} - a_{2} x_{1} - a_{3} x_{2})}{a_{1}}] + b_{2} x_{1} + b_{3} x_{2}$

where,

b₁, b₂, and b₃ are the numerator coefficients of the discrete filter.
a₁, a₂, and a₃ are the denominator coefficients of the discrete filter.

Examples

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Specify a Vector of Initial Conditions for a Discrete Filter Block

Open Model

This example shows how to specify a vector of non-zero initial conditions for the Discrete Filter block.

The Scope shows that with the Initial states of the Discrete Filter block set to [1 2], the difference between the signal filtered by the Discrete Filter block and the signal from the filter's building blocks is zero. This demonstrates that you can enter the initial conditions of the Discrete Filter block as a vector of [1 2]. As an alternative, to achieve the same result, you can set the initial condition of Unit Delay to 1 and Unit Delay1 to 2.

Extended Examples

Model Fault-Tolerant Fuel Control System

Combine Stateflow® and Simulink® capabilities to model hybrid systems. This type of modeling is particularly useful for systems that have numerous possible operational modes based on discrete events. Traditional signal flow is handled in Simulink while changes in control configuration are implemented in Stateflow. The model described in this example represents a fuel control system for a gasoline engine. The system is robust in that it detects individual sensor failures, and the control system is dynamically reconfigured for uninterrupted operation.

Open Model

Ports

Input

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u — Input signal
scalar | vector | matrix

Input signal to filter, 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)

Dependencies

The name of this port depends on the source you specify for the numerator coefficients, denominator coefficients and initial states. When you set Numerator, Denominator, and Initial states to Dialog, there is only one input port, and the port is unlabeled. When you set Numerator, Denominator, or Initial states to Input port, this port is labeled u.

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

Num — Numerator coefficients
scalar | vector

Numerator coefficients of the discrete filter, specified as descending powers of z. Use a row vector to specify the coefficients for a single numerator polynomial.

Dependencies

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

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

Den — Denominator coefficients
scalar | vector

Denominator coefficients of the discrete filter, specified as descending powers of z. Use a row vector to specify the coefficients for a single denominator polynomial.

Dependencies

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

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 — External reset signal
scalar

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.

x0 — Initial states
scalar | vector | matrix

Initial states, specified as a scalar, vector, or matrix. For more information about specifying states, see Specifying Initial States.

Dependencies

To enable this port, set the Filter structure to Direct form II or Direct form II transposed, and set Initial states to Input port.

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

Output

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Port_1 — Filtered output signal
scalar | vector | matrix

Filtered output signal. The output dimensions equal the input dimensions, except when you specify a matrix of filter taps for the Numerator coefficients parameter. When you do so, the output dimensions depend on the number of different sets of filter taps you specify.

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

Filter structure — Filter structure
`Direct form II` (default) | `Direct form I transposed` | `Direct form I` | `Direct form II transposed`

Specify the discrete IIR filter structure.

Dependencies

To use any filter structure other than Direct form II, you must have an available DSP System Toolbox license.

Programmatic Use

Block Parameter: FilterStructure

Type: character vector

Values:

'Direct form II' | 'Direct form I transposed' | 'Direct
										form I' | 'Direct form II transposed'

Default: 'Direct form II'

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

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

Specify the numerator coefficients of the discrete filter as descending powers of z. Use a row vector to specify the coefficients for a single numerator polynomial. To specify coefficients for multiple filters, specify a matrix of coefficients, where each row represents a different set of filter taps. To implement multiple filters, Filter structure must be Direct form II, Input processing must be Elements as channels (sample based), and the input must be a scalar.

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]'

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

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

Specify the denominator coefficients of the discrete filter as descending powers of z. Use a row vector to specify the coefficients for a single denominator polynomial.

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

Default: '[1 0.5]'

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

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'

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

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 the Filter structure to Direct form II or Direct form II transposed, and set Initial states Source to Dialog.

Programmatic Use

Block Parameter: InitialStates

Type: character vector

Values: scalar | vector | matrix

Default: '0'

Alternatively, use IC.

Initial states on numerator side — Initial numerator states
`0` (default) | scalar | vector | matrix

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

Dependencies

To enable this port, set the Filter structure to Direct form I or Direct form I transposed.

Programmatic Use

Block Parameter: InitialStates

Type: character vector

Values: scalar | vector | matrix

Default: '0'

Initial states on denominator side — Initial denominator states
`0` (default) | scalar | vector | matrix

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

Dependencies

To enable this port, set the Filter structure to Direct form I or Direct form I transposed.

Programmatic Use

Block Parameter: InitialDenominatorStates

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

'Level
                        hold'

Default: 'None'

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

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.

Dependencies

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:

'Columns as channels (frame based)' | 'Elements as
										channels (sample based)'

Default:

'Elements as channels (sample
									based)'

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

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'

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

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

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

View Filter Response — View filter response
button

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

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 this parameter 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)' | '<data type
										expression>'

Default: 'Inherit: Same as input'

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

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

A rule that inherits a data type, for example, Inherit: Inherit via internal rule
A built-in signed 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)' |
										'<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. The default 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: 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. The default 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 internal rule` (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 this parameter 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)' | '<data type
									expression>'

Default: 'Inherit: Inherit via internal rule'

Numerator accumulator — Numerator accumulator data type
`Inherit: Inherit via internal rule` (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. You can set this parameter 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)' | '<data
										type expression>'

Default: 'Inherit: Inherit via internal rule'

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

Specify the denominator coefficient data type. You can set this parameter 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)' |
										'<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. The default 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. The default 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 internal rule` (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 this parameter 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)' | '<data type
									expression>'

Default: 'Inherit: Inherit via internal rule'

Denominator accumulator — Denominator accumulator data type
`Inherit: Inherit via internal rule` (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 this parameter 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)' | '<data
										type expression>'

Default: 'Inherit: Inherit via internal rule'

Output — Output data type
`Inherit: Inherit via internal rule` (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 this parameter 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)' | '<data type
										expression>'

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 value is [] (unspecified). Simulink software 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 value is [] (unspecified). Simulink software 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: '[]'

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

Specify the multiplicand data type. You can set this parameter to:

A rule that inherits a data type, for example, Inherit: Same as input
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.

Dependencies

To enable this parameter, set the Filter structure to Direct form I transposed

Programmatic Use

Block Parameter: MultiplicandDataTypeStr

Type: character vector

Values:

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

Default: 'Inherit: Same as input'

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

Select to lock data type settings of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor. For more information, see Lock the Output Data Type Setting (Fixed-Point Designer).

Programmatic Use

Block Parameter: LockScale

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 Modes (Fixed-Point Designer).

Programmatic Use

Block Parameter: RndMeth

Type: character vector

Values:

'Ceiling' | 'Convergent' | 'Floor' |
                                                  'Nearest' | 'Round' | 'Simplest' |
                                                  'Zero'

Default: 'Floor'

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

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

State name — Assign unique name to each state
`' '` (default) | `'position'` | `{'a', 'b', 'c'}` | `a` | ...

Assign a unique name to each state. If this field is blank (' '), no name assignment occurs.

To assign a name to a single state, enter the name between quotes, for example, 'position'.
To assign names to multiple states, enter a comma-delimited list surrounded by braces, for example, {'a', 'b', 'c'}. Each name must be unique.
To assign state names with a variable in the MATLAB^® workspace, enter the variable without quotes. A variable can be a character vector, cell array, or structure.

Limitations

The state names apply only to the selected block.
The number of states must divide evenly among the number of state names.
You can specify fewer names than states, but you cannot specify more names than states.
For example, you can specify two names in a system with four states. The first name applies to the first two states and the second name to the last two states.

Dependencies

To enable this parameter, set Filter structure to Direct form II.

Programmatic Use

Block Parameter: StateName

Type: character vector

Values: ' ' | user-defined

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, set Filter structure to Direct form II and 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`
^a This block only supports signed fixed-point data types.

More About

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Model Coverage

If you have a Simulink Coverage™ license, the Discrete Filter block receives decision coverage if you set the External reset block parameter to any option except for None. If your model uses a State Control (HDL Coder) block, you cannot collect coverage for the external reset port when the State control parameter is Synchronous.

Decision coverage measures a true outcome for time steps where the block resets and a false outcome for time steps where the block does not reset. To receive 100% decision coverage, the block must reset for at least one time step and not reset for at least one time step.

If you select the Saturation on integer overflow (Simulink Coverage) parameter, the Discrete Filter block receives saturation on integer overflow coverage. For more information, see Saturate on Integer Overflow Coverage (Simulink Coverage).

Extended Capabilities

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

This block only supports signed fixed-point data types.

The Discrete Filter block accepts and outputs real and complex signals of any signed numeric data type that Simulink supports. The block supports the same types for the numerator and denominator coefficients.

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

The following diagrams show the filter structure and the data types used within the Discrete Filter block for fixed-point signals.

The block omits the dashed divide when you select the Optimize by skipping divide by leading denominator coefficient (a0) parameter.

Version History

Introduced before R2006a

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R2024b: View filter response

Click the View Filter Response button to visualize the frequency response of the filter that you specify in the block dialog box.

R2024a: The Discrete Filter block supports variable-size input signals

The Discrete Filter block supports variable-size input signals when you set the Input processing parameter to Columns as channels (frame based).

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

R2023b: Conditional display of the Sample time parameter

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

Discrete Filter

Description

Specifying Initial States

Examples

Specify a Vector of Initial Conditions for a Discrete Filter Block

Extended Examples

Model Fault-Tolerant Fuel Control System

Ports

Input

u — Input signal scalar | vector | matrix

Dependencies

Num — Numerator coefficients scalar | vector

Dependencies

Den — Denominator coefficients scalar | vector

Dependencies

External reset — External reset signal scalar

Dependencies

x0 — Initial states scalar | vector | matrix

Dependencies

Output

Port_1 — Filtered output signal scalar | vector | matrix

Parameters

Main

Filter structure — Filter structure Direct form II (default) | Direct form I transposed | Direct form I | Direct form II transposed

Dependencies

Programmatic Use

Numerator Source — Source of numerator coefficients Dialog (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) | vector

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

Initial states on numerator side — Initial numerator states 0 (default) | scalar | vector | matrix

Dependencies

Programmatic Use

Initial states on denominator side — Initial denominator 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 (sample based) (default) | Columns as channels (frame based)

Dependencies

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

View Filter Response — View filter response button

Dependencies

Data Types

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

Programmatic Use

u — Input signal
scalar | vector | matrix

Num — Numerator coefficients
scalar | vector

Den — Denominator coefficients
scalar | vector

External reset — External reset signal
scalar

x0 — Initial states
scalar | vector | matrix

Port_1 — Filtered output signal
scalar | vector | matrix

Filter structure — Filter structure
`Direct form II` (default) | `Direct form I transposed` | `Direct form I` | `Direct form II transposed`

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) | vector

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

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

Initial states on numerator side — Initial numerator states
`0` (default) | scalar | vector | matrix

Initial states on denominator side — Initial denominator 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 (sample based)` (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

View Filter Response — View filter response
button

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 internal rule` (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 internal rule` (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 internal rule` (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 internal rule` (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 internal rule` (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 internal rule` (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 internal rule` (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

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

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 — Assign unique name to each state
`' '` (default) | `'position'` | `{'a', 'b', 'c'}` | `a` | ...

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™.

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

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