Discrete Derivative

Compute discrete-time derivative

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Library:
Simulink / Discrete

Description

TheDiscrete Derivativeblock computes an optionally scaled discrete time derivative as follows

$y (t_{n}) = \frac{K u (t_{n})}{T_{s}} - \frac{K u (t_{n - 1})}{T_{s}}$

where

$u (t_{n})$ and $y (t_{n})$ are the block's input and output at the current time step, respectively.
$u (t_{n - 1})$ is the block's input at the previous time step.
$K$ is a scaling factor.
$T_{s}$ is the simulation's discrete step size, which must be fixed.

Note

Do not use this block in subsystems with a nonperiodic trigger (for example, nonperiodic function-call subsystems). This configuration produces inaccurate results.

Ports

Input

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`Port_1`— Input signal
scalar | vector | matrix

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

Output

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`Port_1`— Scaled discrete time derivative
scalar | vector | matrix

Optionally scaled discrete-time derivative, specified as a scalar, vector, or matrix. For more information on how the block computes the discrete-time derivative, seeDescription. You specify the data type of the output signal with theOutput data typeparameter.

Parameters

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Main

`Gain value`— Scaling factor
`1.0`(default) | scalar

Scaling factor used to weight the block's input at the current time step, specified as a real-valued scalar.

Programmatic Use

Block Parameter:gainval

Type:character vector

Values:scalar

Default:'1.0'

`Initial condition for previous weighted input K*u/Ts`— Initial condition
`0.0`(default) | scalar

Initial condition for the previous scaled input, specified as a scalar.

Programmatic Use

Block Parameter:ICPrevScaledInput

Type:character vector

Values:scalar

Default:'0.0'

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

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

Columns as channels (frame based)— Treat each column of the input as a separate channel (frame-based processing).

Note

Frame-based processing requires a DSP System Toolbox™ license.

For more information, seeSample- and Frame-Based Concepts(DSP System Toolbox).
Elements as channels (sample based)-对每个元素的输入作为一个单独的channel (sample-based processing).
Inherited— Inherit the processing mode from the input signal and delay the input accordingly. You can identify whether the input signal is sample or frame based by looking at the signal line. Simulink^®represents sample-based signals with a single line and frame-based signals with a double line.

Note

When you choose theInheritedoption for theInput processingparameter, and the input signal is frame based, Simulink generates a warning or error in future releases.

UseInput processingto specify whether the block performs sample- or frame-based processing. The block accepts frame-based signals for the inputu. All other input signals must be sample based.

Input Signal u	Input Processing Mode	Block Works?
Sample based	Sample based	Yes
Frame based	Sample based	No, produces an error
Sample based	Frame based	Yes
Frame based	Frame based	Yes
Sample based	Inherited	Yes
Frame based	Inherited	Yes

For more information about these two processing modes, seeSample- 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)'|'Inherited'

Default:'Elements as channels (sample based)'

Signal Attributes

`Output minimum`——最小输出值范围检查
`[]`(default) | scalar

Lower value of the output range that Simulink checks.

Simulink uses the minimum to perform:

Parameter range checking (seeSpecify Minimum and Maximum Values for Block Parameters) for some blocks.
Simulation range checking (seeSignal RangesandEnable Simulation Range Checking).
Automatic scaling of fixed-point data types.
Optimization of the code that you generate from the model. This optimization can remove algorithmic code and affect the results of some simulation modes such as SIL or external mode. For more information, seeOptimize using the specified minimum and maximum values(Simulink Coder).

Note

Output minimumdoes not saturate or clip the actual output signal. Use theSaturationblock instead.

Programmatic Use

Block Parameter:OutMin

Type: character vector

Values:'[ ]'| scalar

Default:'[ ]'

`Output maximum`— Maximum output value for range checking
`[]`(default) | scalar

Upper value of the output range that Simulink checks.

Simulink uses the maximum value to perform:

Parameter range checking (seeSpecify Minimum and Maximum Values for Block Parameters) for some blocks.
Simulation range checking (seeSignal RangesandEnable Simulation Range Checking).
Automatic scaling of fixed-point data types.
Optimization of the code that you generate from the model. This optimization can remove algorithmic code and affect the results of some simulation modes such as SIL or external mode. For more information, seeOptimize using the specified minimum and maximum values(Simulink Coder).

Note

Output maximumdoes not saturate or clip the actual output signal. Use theSaturationblock instead.

Programmatic Use

Block Parameter:OutMax

Type: character vector

Values:'[ ]'| scalar

Default:'[ ]'

`Output data type`— Output data type
`继承:Inherit via internal rule`(default) |`继承:Inherit via back propagation`|`double`|`single`|`int8`|`uint8`|`int16`|`uint16`|`int32`|`uint32`|`fixdt(1,16,0)`|`fixdt(1,16,2^0,0)`

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

A rule that inherits a data type, for example,继承:Inherit via back propagation
The name of a built-in data type, for example,single
The name of a data type object, for example, aSimulink.NumericTypeobject
An expression that evaluates to a data type, for example,fixdt(1,16,0)

Click theShow data type assistantbuttonto display theData Type Assistant, which helps you set the data type attributes. SeeSpecify Data Types Using Data Type Assistantfor more information.

Programmatic Use

Block Parameter:OutDataTypeStr

Type:character vector

Values:

'Inherit: Inherit via internal rule' | 'Inherit: Inherit via back propagation' | 'double' | 'single' | 'int8' | 'uint8' | 'int16' | 'uint16' | 'int32' | 'uint32' | 'fixdt(1,16,0)' | 'fixdt(1,16,2^0,0)'

Default:'Inherit: Inherit via internal rule'

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

Select this parameter to prevent the fixed-point tools from overriding theOutputdata type you specify on the block. For more information, seeUse Lock 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`

For more information, seeRounding(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 to max or min when overflows occur`— Method of overflow action
`off`(default) |`on`

When you select this check box, overflows saturate to the maximum or minimum value that the data type can represent. Otherwise, overflows wrap.

When you select this check box, 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

Block Parameter:DoSatur

Type:character vector

Values:'off' | 'on'

Default:'off'

Model Examples

Discrete-Time Derivative of Floating-Point Input

This example shows how to use the Discrete Derivative block to compute the discrete-time derivative of a floating-point input signal. The unfiltered discrete-time derivative is compared to a filtered discrete-time derivative that is computed by the Discrete Filter block.

Open Model

Fixed-Point Derivatives

This model shows how sample implementations of filtered and unfiltered fixed-point derivative algorithms compare with their floating-point implementations.

Open Model

Block Characteristics

Data Types	`double`\|`single`\|`base integer`\|`fixed point`
Multidimensional Signals	`No`
Variable-Size Signals	`Yes`

Extended Capabilities

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

Depends on absolute time when used inside a triggered subsystem hierarchy.
Generated code relies onmemcpyormemsetfunctions (string.h) under certain conditions.

Documentation

Discrete Derivative

Description

Note

Ports

Input

Port_1— Input signalscalar | vector | matrix

Output

Port_1— Scaled discrete time derivativescalar | vector | matrix

Parameters

Main

Gain value— Scaling factor1.0(default) | scalar

Programmatic Use

Initial condition for previous weighted input K*u/Ts— Initial condition0.0(default) | scalar

Programmatic Use

Input processing— Specify sample- or frame-based processingElements as channels (sample based)(default) |Columns as channels (frame based)|Inherited

Note

Note

Programmatic Use

Signal Attributes

Output minimum——最小输出值范围检查[](default) | scalar

Note

Programmatic Use

Output maximum— Maximum output value for range checking[](default) | scalar

Note

Programmatic Use

Output data type— Output data type继承:Inherit via internal rule(default) |继承:Inherit via back propagation|double|single|int8|uint8|int16|uint16|int32|uint32|fixdt(1,16,0)|fixdt(1,16,2^0,0)

Programmatic Use

Lock output data type setting against changes by the fixed-point tools— Prevent fixed-point tools from overriding Output data typeoff(default) |on

Programmatic Use

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

Programmatic Use

Saturate to max or min when overflows occur— Method of overflow actionoff(default) |on

Programmatic Use

Model Examples

Discrete-Time Derivative of Floating-Point Input

Fixed-Point Derivatives

Block Characteristics

Extended Capabilities

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

PLC Code GenerationGenerate Structured Text code using Simulink® PLC Coder™.

Fixed-Point ConversionConvert floating-point algorithms to fixed point using Fixed-Point Designer™.

See Also

Introduced before R2006a

Simulink Documentation

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`Port_1`— Input signal
scalar | vector | matrix

`Port_1`— Scaled discrete time derivative
scalar | vector | matrix

`Gain value`— Scaling factor
`1.0`(default) | scalar

`Initial condition for previous weighted input K*u/Ts`— Initial condition
`0.0`(default) | scalar

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

`Output minimum`——最小输出值范围检查
`[]`(default) | scalar

`Output maximum`— Maximum output value for range checking
`[]`(default) | scalar

`Output data type`— Output data type
`继承:Inherit via internal rule`(default) |`继承:Inherit via back propagation`|`double`|`single`|`int8`|`uint8`|`int16`|`uint16`|`int32`|`uint32`|`fixdt(1,16,0)`|`fixdt(1,16,2^0,0)`

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

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

`Saturate to max or min when overflows occur`— Method of overflow action
`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
Convert floating-point algorithms to fixed point using Fixed-Point Designer™.