# Fourth-Order Section Filter

Implement cascade of fourth-order section filters

• Library:
• DSP System Toolbox / Filtering / Filter Implementations

## Description

The Fourth-Order Section Filter block implements a cascade of fourth-order section filters in Simulink®. You can specify the numerator and denominator coefficients of the filter in the block parameters dialog box or through input ports.

## Ports

### Input

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Input signal, specified as a vector or a matrix. The input can be a variable size signal. That is, the frame size of the signal can change during simulation but the number of channels cannot.

This port is unnamed until you set the Coefficient source parameter to `Input ports`.

Data Types: `single` | `double`
Complex Number Support: Yes

Specify the numerator coefficients of the fourth-order section filter as a P-by-5 matrix, where P is the number of filter sections. For more details on this input port, see Numerator coefficients of filter.

While the simulation is running, you can change the number of sections (rows) in the numerator coefficients. You can also change the coefficient values.

#### Dependencies

This port appears only when you set the Coefficient source parameter to `Input ports`.

Data Types: `single` | `double`
Complex Number Support: Yes

Specify the denominator coefficients of the fourth-order section filter as a P-by-5 matrix or a P-by-4 matrix, where P is the number of filter sections. For more details on this input port, see Denominator coefficients of filter.

While the simulation is running, you can change the number of sections (rows) in the denominator coefficients. You can also change the coefficient values.

#### Dependencies

This port appears only when you set the Coefficient source parameter to `Input ports`.

Data Types: `single` | `double`
Complex Number Support: Yes

### Output

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Filtered output, returned as a vector or a matrix. The output has the same size and data type as the input. The output signal is complex if either the input signal, numerator coefficients, or the denominator coefficients are complex.

This port is unnamed until you set the Coefficient source parameter to `Input ports`.

Data Types: `single` | `double`
Complex Number Support: Yes

## Parameters

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Specify the filter coefficient source as one of the following:

• `Dialog parameters` –– Specify the filter coefficients through the Numerator coefficients of filter and the Denominator coefficients of filter parameters in the block dialog box.

• `Input ports` –– Specify the filter coefficients through the Num and Den input ports.

• `Filter object` –– Specify the filter coefficients using a `dsp.FourthOrderSectionFilter` object.

To view the filter response, set this parameter to ```Dialog parameters``` or `Filter object`, and then click the button.

Specify the numerator coefficients b of the fourth-order section filter as a P-by-5 matrix, where P is the number of filter sections.

`$b=\left[\begin{array}{ccccc}{b}_{01}& {b}_{11}& {b}_{21}& {b}_{31}& {b}_{41}\\ {b}_{02}& {b}_{12}& {b}_{22}& {b}_{32}& {b}_{42}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ {b}_{0P}& {b}_{1P}& {b}_{2P}& {b}_{3P}& {b}_{4P}\end{array}\right]$`

In the transfer function form, the fourth-order section filter can be represented using the following equation:

`$H\left(z\right)=\prod _{k=1}^{P}{H}_{k}\left(z\right)=\prod _{k=1}^{P}\frac{{b}_{0k}+{b}_{1k}{z}^{-1}+{b}_{2k}{z}^{-2}+{b}_{3k}{z}^{-3}+{b}_{4k}{z}^{-4}}{{a}_{0k}+{a}_{1k}{z}^{-1}+{a}_{2k}{z}^{-2}+{a}_{3k}{z}^{-3}+{a}_{4k}{z}^{-4}}$`

where,

• a –– Denominator coefficients matrix. For more details on how to specify this matrix, see Denominator coefficients of filter.

• k –– Row index.

You cannot change the size of this parameter during simulation, but you can change its value.

Tunable: Yes

#### Dependencies

To enable this parameter, set Coefficient source to `Dialog parameters`.

Data Types: `single` | `double`
Complex Number Support: Yes

Specify the denominator coefficients a of the fourth-order section filter as a P-by-5 matrix or a P-by-4 matrix, where P is the number of filter sections.

`$a=\left[\begin{array}{ccccc}{a}_{01}& {a}_{11}& {a}_{21}& {a}_{31}& {a}_{41}\\ {a}_{02}& {a}_{12}& {a}_{22}& {a}_{32}& {a}_{42}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ {a}_{0P}& {a}_{1P}& {a}_{2P}& {a}_{3P}& {a}_{4P}\end{array}\right]$`

The block algorithm assumes that the value of the leading coefficients is always 1. If the denominator is of size P-by-4, the block algorithm places 1s in the first column to make the denominator size P-by-5. If the denominator is of size P-by-5 and the elements in the first column do not equal 1, the algorithm ignores the values in the first column and appends them with 1s.

In the transfer function form, the fourth-order section filter can be represented using the following equation:

`$H\left(z\right)=\prod _{k=1}^{P}{H}_{k}\left(z\right)=\prod _{k=1}^{P}\frac{{b}_{0k}+{b}_{1k}{z}^{-1}+{b}_{2k}{z}^{-2}+{b}_{3k}{z}^{-3}+{b}_{4k}{z}^{-4}}{{a}_{0k}+{a}_{1k}{z}^{-1}+{a}_{2k}{z}^{-2}+{a}_{3k}{z}^{-3}+{a}_{4k}{z}^{-4}}$`

where,

• b –– Numerator coefficients matrix. For more details on how to specify this matrix, see Numerator coefficients of filter.

• k –– Row index.

You cannot change the size of this parameter during simulation, but you can change its value.

Tunable: Yes

#### Dependencies

To enable this parameter, set Coefficient source to `Dialog parameters`.

Data Types: `single` | `double`
Complex Number Support: Yes

Specify the filter coefficients using a `dsp.FourthOrderSectionFilter` object. You can enter this object directly in the Filter parameter. Alternatively, you can create this object in the MATLAB® workspace or model workspace and specify the filter variable in the Filter parameter. When you specify the filter as a variable and you simulate the model, you cannot change the complexity, data type, and size of the filter coefficients in the workspace between simulations.

#### Dependencies

To enable this parameter, set Coefficient source to `Filter object`.

Click this button to open the Dynamic Filter Visualizer window and display the magnitude and phase response of the fourth-order section filter. The response is based on the coefficients that you specify in the block dialog box. If you set Coefficient source to `Input ports` and click , you cannot view the magnitude response using this button. To view the response in the visualizer, you must specify the filter coefficients directly in the block dialog box or through the `dsp.FourthOrderSectionFilter` object.

To update the filter response while the visualizer is running, modify the coefficients in the block dialog box and click .

You can configure the plot settings and the frequency response measurements from the interface of the visualizer.

On the Plot tab, you can enable the legend, specify to plot both magnitude and phase responses of the filter, modify the plot settings, generate a script to re-create the plot, and even save or share the settings.

On the Measurements tab, you can enable data cursors, and display the peak values of the filter response.

For more details on the Dynamic Filter Visualizer interface and its tools, see Configure Dynamic Filter Visualizer.

Type of simulation to run. You can set this parameter to:

• `Interpreted execution`: Simulate model using the MATLAB interpreter. This option shortens startup time.

• `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.

## Block Characteristics

 Data Types `double` | `integer` | `single` Direct Feedthrough `no` Multidimensional Signals `no` Variable-Size Signals `yes` Zero-Crossing Detection `no`

## Version History

Introduced in R2022a

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