Differentiator Filter
Direct form FIR fullband differentiator filter
Libraries:
DSP System Toolbox /
Filtering /
Filter Designs
Description
The Differentiator Filter block applies a fullband differentiator filter on the input signal to differentiate all its frequency components. The block uses an FIR equiripple filter design to design the differentiator filter. The ideal frequency response of the differentiator is $$D(\omega )=j\omega $$ for $$\pi \le \omega \le \pi $$.
You can design the filter with a minimum order or with a specific order.
This block also supports SIMD code generation. For details, see Code Generation.
Examples
Ports
Input
Input — Data input
vector  matrix
Specify the data input as a vector or a matrix. If the input signal is a matrix, each column of the matrix is treated as an independent channel.
This block supports variablesize input, enabling you to change the channel length during simulation.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
Complex Number Support: Yes
Output
Output — Differentiator filter output
vector  matrix
Differentiator filter output, returned as a vector or a matrix.
The output port properties, such as data type, complexity, and dimension are identical to the input port properties.
Data Types: single
 double
 fixed point
Complex Number Support: Yes
Parameters
Main Tab
Design minimum order filter — Design minimum order filter
on
(default)  off
When you select this check box, the block designs a filter with the minimum order and with the passband ripple that you specify in Maximum passband ripple (dB). When you clear this check box, specify the order of the filter in Filter order.
Filter order — Order of differentiator filter
31
(default)  odd positive integer
Specify the order of the differentiator filter as an odd positive integer.
Dependencies
To enable this parameter, clear the Design minimum order filter parameter.
Maximum passband ripple (dB) — Maximum passband ripple
0.1
(default)  positive scalar
Specify the maximum ripple of the filter response in the passband as a real positive scalar in dB.
Scale filter coefficients — Scale filter coefficients
off
(default)  on
When you select this check box, the blocks scales the filter coefficients to preserve the input dynamic range. By default, this check box is not selected.
View Filter Response — View filter response
button (default)
Click this button to open the Filter Visualization Tool
(fvtool
) and display the magnitude and phase
response of the Differentiator Filter block. The response
is based on the block dialog box parameters. Changes made to these
parameters update FVTool.
To update the magnitude response while FVTool is running, modify the dialog box parameters and click Apply.
Simulate using — Simulate using
Interpreted
execution
(default)  Code generation
Specify the type of simulation to run. You can set this parameter to:
Interpreted execution
(default)Simulate model using the MATLAB^{®} interpreter. This option shortens startup time and has faster simulation speed than
Code generation
.Code generation
Simulate model using generated C code. The first time you run a simulation, Simulink^{®} generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time but provides faster subsequent simulations.
Data Types Tab
Rounding mode — Rounding mode
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Specify the rounding method for the output fixedpoint operations. The rounding methods
are Ceiling
,
Convergent
,
Floor
,
Nearest
, Round
,
Simplest
, and
Zero
. The default is
Floor
.
Coefficients — Coefficients
fixdt(1,16)
(default)  fixdt(1,16,0)
 <data type expression>
Specify the fixedpoint data type of the coefficients as one of the following:
fixdt(1,16)
— Signed fixedpoint data type of word length16
with binary point scaling. The block determines the fraction length automatically from the coefficient values such that the coefficients occupy the maximum representable range without overflowing.fixdt(1,16,0)
— Signed fixedpoint data type of word length16
and fraction length0
. You can change the fraction length to any other integer value.<data type expression>
— Specify the data type using an expression that evaluates to a data type object, for example, numeric type (fixdt
([ ]
,16
,15
)). Specify the sign mode of this data type as[ ]
ortrue
.Refresh Data Type
— Refresh to the default data type.
Click the Show data type assistant button to display the data type assistant, which helps you set the stage input parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
The word length of the output is same as the word length of the input. The fraction length of the output is computed such that the entire dynamic range of the output can be represented without overflow. For details on how the block computes the fraction length, see FixedPoint Precision Rules for Avoiding Overflow in FIR Filters.
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

Algorithms
Differentiator Filter
Differentiator computes the derivative of a signal. The frequency response of an ideal differentiator filter is given by $$D(\omega )=j\omega $$, defined over the Nyquist interval $$\pi \le \omega \le \pi $$.
The frequency response is antisymmetric and is linearly proportional to the frequency.
dsp.Differentiator
object acts as a differentiator
filter. This object condenses the twostep process into one. For the
minimum order design, the object uses generalized Remez FIR filter
design algorithm. For the specified order design, the object uses
the ParksMcClellan optimal equiripple FIR filter design algorithm.
The filter is designed as a linear phase TypeIV FIR filter with a
Direct form structure.
The ideal differentiator has an antisymmetric impulse response given by $$d(n)=d(n)$$. Hence $$d(0)=0$$. The differentiator must have zero response at zero frequency.
LinearPhase FIR Differentiator Filter
The impulse response of an antisymmetric linearphase FIR filter is given by $$h(n)=h(M1n)$$, where M is the length of the filter. Because the filter is antisymmetric, you can use this type of FIR filter to design the linearphase FIR differentiators.
Consider the design of linearphase FIR differentiators based on the Chebyshev approximation criterion.
If M is odd, the realvalued frequency response of the FIR filter, H_{r}(ω), has the characteristics that H_{r}(0) = 0 and H_{r}(π) = 0. This filter satisfies the condition of zero response at zero frequency. However, it is not fullband because H_{r}(π) = 0. This differentiator has a linear response over the limited frequency range [0 2πf_{p}], where f_{p} is the bandwidth of the differentiator. The absolute error between the desired response and the Chebyshev approximation increases as ω increases from 0 to 2πf_{p}.
If M is even, the realvalued frequency response of the FIR filter, H_{r}(ω), has the characteristics that H_{r}(0) = 0 and H_{r}(π) ≠ 0. This filter satisfies the condition of zero response at zero frequency. It is fullband and this design results in a significantly smaller approximation error than comparable oddlength differentiators. Hence, evenlength (odd order) differentiators are preferred in practical systems.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
The Differentiator Filter block supports SIMD code generation using
Intel AVX2 code replacement library when the input signal has a data type of
single
or double
.
The SIMD technology significantly improves the performance of the generated code. For more information, see SIMD Code Generation. To generate SIMD code from this block, see Use Intel AVX2 Code Replacement Library to Generate SIMD Code from Simulink Blocks.
Version History
Introduced in R2015b
See Also
Objects
Blocks
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