Discrete Derivative

Compute discrete-time derivative

• Library:

• Simulink / Discrete

Description

The Discrete Derivative block computes an optionally scaled discrete time derivative as follows

$$y(t_n)=\frac{Ku(t_n)}{T_s}-\frac{Ku(t_{n-1})}{T_s}$$

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

Port_1 — Input signal

scalar | vector | matrix

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

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | fixed point

Output

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, see Description. You specify the data type of the output signal with the Output data type parameter.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | fixed point

Parameters

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)

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, see Sample- and Frame-Based Concepts (DSP System Toolbox).

• Elements as channels (sample based) — Treat each element of the input as a separate channel (sample-based processing).

Use Input processing to specify whether the block performs sample- or frame-based processing. The block accepts frame-based signals for the input u. All other input signals must be sample-based.

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

For more information about these two processing modes, 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)'

Signal Attributes

Output minimum — Minimum output value for range checking

[] (default) | scalar

Lower value of the output range that Simulink^® checks.

Simulink uses the minimum to perform:

• Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters) for some blocks.

• Simulation range checking (see Signal Ranges and Enable 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, see Optimize using the specified minimum and maximum values (Simulink Coder).

Note

Output minimum does not saturate or clip the actual output signal. Use the Saturation block 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 (see Specify Minimum and Maximum Values for Block Parameters) for some blocks.

• Simulation range checking (see Signal Ranges and Enable 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, see Optimize using the specified minimum and maximum values (Simulink Coder).

Note

Output maximum does not saturate or clip the actual output signal. Use the Saturation block instead.

Programmatic Use

Block Parameter: OutMax

Type: character vector

Values: '[ ]'| scalar

Default: '[ ]'

Output data type — Output data type

Inherit: Inherit via internal rule (default) | Inherit: 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, Inherit: Inherit via back propagation

• The name of a built-in data type, for example, single

• The name of a data type object, for example, a Simulink.NumericType object

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

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. 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: 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 the Output data type you specify on the block. For more information, see Use 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

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

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

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.

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
Direct Feedthrough	No
Multidimensional Signals	No
Variable-Size Signals	Yes
Zero-Crossing Detection	No

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 on memcpy or memset functions (string.h) under certain conditions.

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™.