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Hilbert Filter

Design Hilbert filter


Filtering / Filter Designs


  • Hilbert Filter block


This block brings the filter design capabilities of the filterBuilder function to the Simulink® environment.

This block supports SIMD code generation. For details, see Code Generation.

Dialog Box

See Hilbert Filter Design — Main Pane for more information about the parameters of this block. The Data Types and Code panes are not available for blocks in the DSP System Toolbox™ Filter Designs library.

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.

Filter Specifications

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.


The design methods and structures for FIR filters are not the same as the methods and structures for IIR filters.

Filter order mode

Select either Minimum (the default) or Specify from the drop-down list. Selecting Specify enables the Order option (see the following sections) so you can enter the filter order.

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.


Enter the filter order. This option is enabled only if Specify was selected for Filter order mode.

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.

Frequency Specifications

The parameters in this group allow you to specify your filter response curve.

Frequency units

Use this parameter to specify whether your frequency settings are normalized or in absolute frequency. Select Normalized (0 to 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

Fs, 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.

Transition width

Specify the width of the transitions at the ends of the passband. Specify the value in normalized frequency units or the absolute units you select in Frequency units.

Magnitude Specifications

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

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)

  • Squared — Specify the magnitude in squared units.

Passband ripple

Enter the filter ripple allowed in the passband 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 FIR method is Equiripple.

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 20 represents a reasonable trade between the accurate approximation to the ideal filter and the time to design the filter.

FIR Type

Specify whether to design a type 3 or a type 4 FIR filter. The filter type is defined as follows:

  • Type 3 — FIR filter with even order antisymmetric coefficients

  • Type 4 — FIR filter with odd order antisymmetric coefficients

Select either 3 or 4 from the drop-down list.

Filter Implementation


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 FIR, and IIR filters use Cascade minimum-multiplier allpass.

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.

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.

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 variable 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.

Supported Data Types

PortSupported Data Types


  • Double-precision floating point

  • Single-precision floating point


  • Double-precision floating point

  • Single-precision floating point

Extended Capabilities

Version History

Introduced in R2006b