## Documentation Center |

Design lowpass filter

This block brings the filter design capabilities of the ` filterbuilder` function
to the Simulink

**View filter response**This button opens the Filter Visualization Tool (

`fvtool`) from the Signal Processing Toolbox™ product. You can use the tool to display:Magnitude response, phase response, and group delay in the frequency domain.

Impulse response and step response in the time domain.

Pole-zero information.

The tool also helps you evaluate filter performance by providing information about filter order, stability, and phase linearity. For more information on FVTool, see the Signal Processing Toolbox documentation.

In this group, you specify your filter format, such as the impulse response and the filter order.

**Impulse response**Select either

`FIR`or`IIR`from the drop-down list.`FIR`is the default. When you choose an impulse response, the design methods and structures you can use to implement your filter change accordingly.**Order mode**Select

`Minimum`(the default) or`Specify`. Selecting`Specify`enables the**Order**option so you can enter the filter order. When you set the**Impulse response**to`IIR`, you can specify different numerator and denominator orders. To specify a different denominator order, you must select the**Denominator order**check box.**Order**Enter the filter order. This option is enabled only if you set the

**Order mode**to`Specify`.**Denominator order**Select this check box to specify a different denominator order. This option is enabled only if you set the

**Impulse response**to`IIR`and the**Order mode**to`Specify`.**Filter type**Select

`Single-rate`,`Decimator`,`Interpolator`, or`Sample-rate converter`. Your choice determines the type of filter as well as the design methods and structures that are available to implement your filter. By default, the block specifies a single-rate filter.Selecting

`Decimator`or`Interpolator`activates the**Decimation Factor**or the**Interpolation Factor**options respectively.Selecting

`Sample-rate converter`activates both factors.

**Decimation Factor**Enter the decimation factor. This option is enabled only if the

**Filter type**is set to`Decimator`or`Sample-rate converter`. The default value is 2.**Interpolation Factor**Enter the interpolation factor. This option is enabled only if the

**Filter type**is set to`Interpolator`or`Sample-rate converter`. The default value is 2.

The parameters in this group allow you to specify your filter response curve. Graphically, the filter specifications look similar to the one shown in the following figure.

In the figure, regions between specification values such as
F_{pass} and F_{stop} represent
transition regions where the filter response is not constrained.

**Frequency constraints**When

**Order mode**is`Specify`, select the filter features that the block uses to define the frequency response characteristics. The list contains the following options, when available for the filter specifications.`Passband and Stopband frequencies`— Define the filter by specifying the frequencies for the edges for the stop- and passbands.`Passband frequency`— Define the filter by specifying the edge of the passband.`Stopband frequency`— Define the filter by specifying the edge of the stopband.`Hafband power (3dB) frequency`— Define the filter response by specifying the location of the 3 dB point. The 3 dB point is the frequency for the point three decibels below the passband value.`Cutoff (6dB) frequency`— For FIR filters, define the filter response by specifying the location of the 6 dB point. The 6 dB point is the frequency for the point six decibels below the passband value.

**Frequency units**Use this parameter to specify whether your frequency settings are normalized or in absolute frequency. Select

`Normalized (0–1)`to enter frequencies in normalized form. This behavior is the default. To enter frequencies in absolute values, select one of the frequency units from the drop-down list—`Hz`,`kHz`,`MHz`, or`GHz`. Selecting one of the unit options enables the**Input sample rate**parameter.**Input sample rate****Input sample rate**, specified in the units you selected for**Frequency units**, defines the sampling frequency at the filter input. When you provide an input sampling frequency, all frequencies in the specifications are in the selected units as well. This parameter is available when you select one of the frequency options from the**Frequency units**list.**Passband frequency**Enter the frequency at the end of the passband. Specify the value in either normalized frequency units or the absolute units you select in

**Frequency units**.**Stopband frequency**Enter the frequency at the start of the stopband. Specify the value in either normalized frequency units or the absolute units you select in

**Frequency units**.**Half power (3dB) frequency**When

**Frequency constraints**is`Half power (3dB) frequency`, specify the frequency of the 3 dB point. Specify the value in either normalized frequency units or the absolute units you select in**Frequency units**.**Cutoff (6dB) frequency**When

**Frequency constraints**is`Cutoff (6dB) frequency`, specify the frequency of the 6 dB point. Specify the value in either normalized frequency units or the absolute units you select**Frequency units**.

Parameters in this group specify the filter response in the passbands and stopbands.

**Magnitude constraints**This option is only available when you specify the order of your filter design. Depending on the setting of the

**Frequency constraints**parameter, some combination of the following options will be available for the**Magnitude constraints**parameter:`Unconstrained`, and`Passband ripple and stopband attenuation`.**Magnitude units**Specify the units for any parameter you provide in magnitude specifications. From the drop-down list, select one of the following options:

`Linear`— Specify the magnitude in linear units.`dB`— Specify the magnitude in decibels (default)

**Passband ripple**Enter the filter ripple allowed in the passband in the units you choose for

**Magnitude units**, either linear or decibels.**Stopband attenuation**Enter the filter attenuation in the stopband in the units you choose for

**Magnitude units**, either linear or decibels.

The parameters in this group allow you to specify the design method and structure of your filter.

**Design Method**Lists the design methods available for the frequency and magnitude specifications you entered. When you change the specifications for a filter, such as changing the impulse response, the methods available to design filters changes as well. The default IIR design method is usually

`Elliptic`, and the default FIR method is`Equiripple`.**Scale SOS filter coefficients to reduce chance of overflow**Selecting this parameter directs the design to scale the filter coefficients to reduce the chances that the inputs or calculations in the filter overflow and exceed the representable range of the filter. Clearing this option removes the scaling. This parameter applies only to IIR filters.

**Design Options**The options for each design are specific for each design method. This section does not present all of the available options for all designs and design methods. There are many more that you encounter as you select different design methods and filter specifications. The following options represent some of the most common ones available.

**Density factor**Density factor controls the density of the frequency grid over which the design method optimization evaluates your filter response function. The number of equally spaced points in the grid is the value you enter for

**Density factor**times (filter order + 1).Increasing the value creates a filter that more closely approximates an ideal equiripple filter but increases the time required to design the filter. The default value of 16 represents a reasonable trade between the accurate approximation to the ideal filter and the time to design the filter.

**Phase constraint**Specify the phase constraint of the filter as

`Linear`,`Maximum`, or`Minimum`.**Minimum order**When you select this parameter, the design method determines and design the minimum order filter to meet your specifications. Some filters do not provide this parameter. Select

`Any`,`Even`, or`Odd`from the drop-down list to direct the design to be any minimum order, or minimum even order, or minimum odd order.**Match Exactly**Specifies that the resulting filter design matches either the passband or stopband or both bands when you select

`passband`or`stopband`or`both`from the drop-down list.**Stopband Shape**Stopband shape lets you specify how the stopband changes with increasing frequency. Choose one of the following options:

`Flat`— Specifies that the stopband is flat. The attenuation does not change as the frequency increases.`Linear`— Specifies that the stopband attenuation changes linearly as the frequency increases. Change the slope of the stopband by setting**Stopband decay**.`1/f`— Specifies that the stopband attenuation changes exponentially as the frequency increases, where`f`is the frequency. Set the power (exponent) for the decay in**Stopband decay**.

**Stopband Decay**When you set Stopband shape, Stopband decay specifies the amount of decay applied to the stopband. the following conditions apply to Stopband decay based on the value of Stopband Shape:

When you set

**Stopband shape**to`Flat`,**Stopband decay**has no affect on the stopband.When you set

**Stopband shape**to`Linear`, enter the slope of the stopband in units of dB/rad/s. The block applies that slope to the stopband.When you set

**Stopband shape**to`1/f`, enter a value for the exponent*n*in the relation (1/f)^{n}to define the stopband decay. The block applies the (1/f)^{n}relation to the stopband to result in an exponentially decreasing stopband attenuation.

**Structure**For the filter specifications and design method you select, this parameter lists the filter structures available to implement your filter. By default, FIR filters use direct-form structure, and IIR filters use direct-form II filters with SOS.

**Use basic elements to enable filter customization**Select this check box to implement the filter as a subsystem of basic Simulink blocks. Clear the check box to implement the filter as a high-level subsystem. By default, this check box is cleared.

The high-level implementation provides better compatibility across various filter structures, especially filters that would contain algebraic loops when constructed using basic elements. On the other hand, using basic elements enables the following optimization parameters:

**Optimize for zero gains**— Terminate chains that contain Gain blocks with a gain of zero.**Optimize for unit gains**— Remove Gain blocks that scale by a factor of one.**Optimize for delay chains**— Substitute delay chains made up of*n*unit delays with a single delay by*n*.**Optimize for negative gains**— Use subtraction in Sum blocks instead of negative gains in Gain blocks.

**Optimize for unit scale values**Select this check box to scale unit gains between sections in SOS filters. This parameter is available only for SOS filters (Impulse response: IIR).

**Input processing**Specify how the block should process the input. The available options may vary depending on he settings of the

**Filter Structure**and**Use basic elements for filter customization**parameters. You can set this parameter to one of the following options:`Columns as channels (frame based)`— When you select this option, the block treats each column of the input as a separate channel.`Elements as channels (sample based)`— When you select this option, the block treats each element of the input as a separate channel.

**Note:**The`Inherited (this choice will be removed — see release notes)`option will be removed in a future release. See Frame-Based Processing in the*DSP System Toolbox™ Release Notes*for more information.**Rate options**When the

**Filter type**parameter specifies a multirate filter, select the rate processing rule for the block from following options:`Enforce single-rate processing`— When you select this option, the block maintains the sample rate of the input.`Allow multirate processing`— When you select this option, the block adjusts the rate at the output to accommodate an increased or reduced number of samples. To select this option, you must set the**Input processing**parameter to`Elements as channels (sample based)`.

**Use symbolic names for coefficients**Select this check box to enable the specification of coefficients using MATLAB

^{®}variables. The available coefficient names differ depending on the filter structure. Using symbolic names allows tuning of filter coefficients in generated code. By default, this check box is cleared.

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