Overview of Filter Designer Features

DSP System Toolbox™ software adds new dialog boxes and operating modes, and new menu selections, to the filter designer provided by Signal Processing Toolbox™ software. From the additional dialog boxes, one titled Set Quantization Parameters and one titled Frequency Transformations, you can:

After you import a filter into filter designer, the options on the quantization dialog box let you quantize the filter and investigate the effects of various quantization settings.

Options in the frequency transformations dialog box let you change the frequency response of your filter, keeping various important features while changing the response shape.

Use Filter Designer with DSP System Toolbox Software

Adding DSP System Toolbox software to your tool suite adds a number of filter design techniques to filter designer. Use the new filter responses to develop filters that meet more complex requirements than those you can design in Signal Processing Toolbox software. While the designs in filter designer are available as command line functions, the graphical user interface of filter designer makes the design process more clear and easier to accomplish.

As you select a response type, the options in the right panes in filter designer change to let you set the values that define your filter. You also see that the analysis area includes a diagram (called a design mask) that describes the options for the filter response you choose.

By reviewing the mask you can see how the options are defined and how to use them. While this is usually straightforward for lowpass or highpass filter responses, setting the options for the arbitrary response types or the peaking/notching filters is more complicated. Having the masks leads you to your result more easily.

Changing the filter design method changes the available response type options. Similarly, the response type you select may change the filter design methods you can choose.

Design a Notch Filter

Notch filters aim to remove one or a few frequencies from a broader spectrum. You must specify the frequencies to remove by setting the filter design options in filter designer appropriately:

Here is how you design a notch filter that removes concert A (440 Hz) from an input musical signal spectrum.

When you design a single notch filter, you do not have the option of setting the filter order — the Filter Order options are disabled.

Your filter should look about like this:

For more information about a design method, refer to the online Help system. For instance, to get further information about the Q setting for the notch filter in filter designer, enter

doc designNotchPeakIIR

at the command line. This opens the Help browser and displays the reference page for function designNotchPeakIIR.

Designing other filters follows a similar procedure, adjusting for different design specification options as each design requires.

Any one of the designs may be quantized in filter designer and analyzed with the available analyses on the Analysis menu.

Set Quantization Parameters

Quantized filters have properties that define how they quantize data you filter. Use the Set Quantization Parameters dialog box in filter designer to set the properties. Using options in the Set Quantization Parameters dialog box, filter designer lets you perform a number of tasks:

When you click Set Quantization Parameters, and then change Filter arithmetic to Fixed-point, the quantized filter panel opens in filter designer, with the coefficient quantization options set to default values.

Coefficients Options

To let you set the properties for the filter coefficients that make up your quantized filter, filter designer lists options for numerator word length (and denominator word length if you have an IIR filter). The following table lists each coefficients option and a short description of what the option setting does in the filter.

Input/Output Options

The options that specify how the quantized filter uses input and output values are listed in the table below.

Filter Internals Options

The options that specify how the quantized filter performs arithmetic operations are listed in the table below.

Filter Internals Options for CIC Filters

CIC filters use slightly different options for specifying the fixed-point arithmetic in the filter. The next table shows and describes the options.

Quantize Double-Precision Filters.  When you are quantizing a double-precision filter by switching to fixed-point or single-precision floating point arithmetic, follow these steps.

Change the Quantization Properties of Quantized Filters.  When you are changing the settings for the quantization of a quantized filter, or after you import a quantized filter from your MATLAB workspace, follow these steps to set the property values for the filter:

Analyze Filters with the Magnitude Response Estimate Method

After you design and quantize your filter, the Magnitude Response Estimate option on the Analysis menu lets you apply the noise loading method to your filter. When you select Analysis > Magnitude Response Estimate from the menu bar, filter designer immediately starts the Monte Carlo trials that form the basis for the method and runs the analysis, ending by displaying the results in the analysis area in filter designer.

With the noise-based method, you estimate the complex frequency response for your filter as determined by applying a noise- like signal to the filter input. Magnitude Response Estimate uses the Monte Carlo trials to generate a noise signal that contains complete frequency content across the range 0 to Fs. The first time you run the analysis, magnitude response estimate uses default settings for the various conditions that define the process, such as the number of test points and the number of trials.

After your first analysis run ends, open the Analysis Parameters dialog box and adjust your settings appropriately, such as changing the number of trials or number of points.

To open the Analysis Parameters dialog box, use either of the next procedures when you have a quantized filter in filter designer:

Whichever option you choose opens the dialog box. Notice that the settings for the options reflect the defaults.

Noise Method Applied to a Filter.  To demonstrate the magnitude response estimate method, start by creating a quantized filter. For this example, use filter designer to design a sixth-order Butterworth IIR filter.

To Use Noise-Based Analysis in Filter Designer

View the Noise Power Spectrum.  When you use the noise method to estimate the magnitude response of a filter, filter designer simulates and applies a spectrum of noise values to test your filter response. While the simulated noise is essentially white, you might want to see the actual spectrum that filter designer used to test your filter.

From the Analysis menu bar option, select Round-off Noise Power Spectrum. In the analysis area in filter designer, you see the spectrum of the noise used to estimate the filter response. The details of the noise spectrum, such as the range and number of data points, appear in the Analysis Parameters dialog box.

For more information, refer to McClellan, et al., Computer-Based Exercises for Signal Processing Using MATLAB 5, Prentice-Hall, 1998. See Project 5: Quantization Noise in Digital Filters, page 231.

Change Your Noise Analysis Parameters.  In Noise Method Applied to a Filter, you used synthetic white noise to estimate the magnitude response for a fixed-point highpass Butterworth filter. Since you ran the estimate only once in filter designer, your noise analysis used the default analysis parameters settings shown in Analyze Filters with the Magnitude Response Estimate Method.

To change the settings, follow these steps after the first time you use the noise estimate on your quantized filter.

Compare the Estimated and Theoretical Magnitude Responses

An important measure of the effectiveness of the noise method for estimating the magnitude response of a quantized filter is to compare the estimated response to the theoretical response.

One way to do this comparison is to overlay the theoretical response on the estimated response. While you have the Magnitude Response Estimate displaying in filter designer, select Analysis > Overlay Analysis from the menu bar. Then select Magnitude Response to show both response curves plotted together in the analysis area.

Select Quantized Filter Structures

Filter designer lets you change the structure of any quantized filter. Use the Convert structure option to change the structure of your filter to one that meets your needs.

To learn about changing the structure of a filter in filter designer, refer to Converting the Filter Structure.

Convert the Structure of a Quantized Filter

You use the Convert structure option to change the structure of filter. When the Source is Designed(Quantized) or Imported(Quantized), Convert structure lets you recast the filter to one of the following structures:

Starting from any quantized filter, you can convert to one of the following representation:

Additionally, filter designer lets you do the following conversions:

Convert Filters to Second-Order Sections Form

To learn about using filter designer to convert your quantized filter to use second-order sections, refer to Converting to Second-Order Sections. You might notice that filters you design in filter designer, rather than filters you imported, are implemented in SOS form.

View Filter Structures in Filter Designer.  To open the demonstration, click Help > Show Filter Structure. After the Help browser opens, you see the reference page for the current filter. You find the filter structure signal flow diagram on this reference page, or you can navigate to reference pages for other filter.

Use the Reordering and Scaling of Second-Order Sections Dialog Box

Filter designer provides the ability to scale SOS filters after you create them. Using options on the Reordering and Scaling of Second-Order Sections dialog box, filter designer scales either or both the filter numerators and filter scale values according to your choices for the scaling options.

Various combinations of settings let you scale filter numerators without changing the scale values, or adjust the filter scale values without changing the numerators. There is no scaling control for denominators.

Scale an SOS Filter

Start the process by designing a lowpass elliptical filter in filter designer.

With the coefficients displayed you can see the effects of scaling your filter directly in the scale values and filter coefficients.

Now try scaling the filter in a few different ways. First scale the filter to maximize the SNR.

Reorder Filters Using Filter Designer

Filter Designer designs most discrete-time filters in second-order sections. Generally, SOS filters resist the effects of quantization changes when you create fixed-point filters. After you have a second-order section filter in filter designer, either one you designed in the tool, or one you imported, filter designer provides the capability to change the order of the sections that compose the filter. Any SOS filter in filter designer allows reordering of the sections.

To reorder the sections of a filter, you access the Reorder and Scaling of Second-Order Sections dialog box in filter designer.

With your SOS filter in filter designer, select Edit > Reorder and Scale from the menu bar. filter designer returns the reordering dialog box shown here with the default settings.

In this dialog box, the left-hand side contains options for reordering SOS filters. On the right you see the scaling options. These are independent — reordering your filter does not require scaling (note the Scale option) and scaling does not require that you reorder your filter (note the None option under Reordering). For more about scaling SOS filters, refer to Scale Second-Order Section Filters and to scale in the reference section.

Reordering SOS filters involves using the options in the Reordering and Scaling of Second-Order Sections dialog box. The following table lists each reorder option and provides a description of what the option does.

Reorder an SOS Filter.  With filter designer open a second-order filter as the current filter, you use the following process to access the reordering capability and reorder you filter. Start by launching filter designer from the command prompt.

Now you are ready to reorder the sections of your filter. Note that filter designer performs the reordering on the current filter in the session.

Use Least Selective to Most Selective Section Reordering.  To let filter designer reorder your filter so the least selective section is first and the most selective section is last, perform the following steps in the Reordering and Scaling of Second-Order Sections dialog box.

You see what reordering does, although the result is a bit subtle. Now try custom reordering the sections of your filter or using the most selective to least selective reordering option.

Using the SOS View Dialog Box

Since you can design and reorder the sections of SOS filters, filter designer provides the ability to view the filter sections in the analysis area — SOS View. Once you have a second-order section filter as your current filter in filter designer, you turn on the SOS View option to see the filter sections individually, or cumulatively, or even only some of the sections. Enabling SOS View puts filter designer in a mode where all second-order section filters display sections until you disable the SOS View option. SOS View mode applies to any analysis you display in the analysis area. For example, if you configure filter designer to show the phase responses for filters, enabling SOS View means filter designer displays the phase response for each section of SOS filters.

Controls on the SOS View Dialog Box

SOS View uses a few options to control how filter designer displays the sections, or which sections to display. When you select View > SOS View from the filter designer menu bar, you see this dialog box containing options to configure SOS View operation.

By default, SOS View shows the overall response of SOS filters. Options in the SOS View dialog box let you change the display. This table lists all the options and describes the effects of each.

View the Sections of SOS Filters

After you design or import an SOS filter in to filter designer, the SOS view option lets you see the per section performance of your filter. Enabling SOS View from the View menu in filter designer configures the tool to display the sections of SOS filters whenever the current filter is an SOS filter.

These next steps demonstrate using SOS View to see your filter sections displayed in filter designer.

Overview and Structures

When you import a quantized filter into filter designer, or export a quantized filter from filter designer to your workspace, the import and export functions use objects and you specify the filter as a variable. This contrasts with importing and exporting nonquantized filters, where you select the filter structure and enter the filter numerator and denominator for the filter transfer function.

You have the option of exporting quantized filters to your MATLAB workspace, exporting them to text files, or exporting them to MAT-files.

For general information about importing and exporting filters in filter designer, refer to Importing a Filter Design, and Exporting a Filter Design.

Filter designer imports quantized filters having the following structures:

Import Quantized Filters

After you design or open a quantized filter in your MATLAB workspace, filter designer lets you import the filter for analysis. Follow these steps to import your filter in to filter designer:

To Export Quantized Filters

To save your filter design, filter designer lets you export the quantized filter to your MATLAB workspace (or you can save the current session in filter designer). When you choose to save the quantized filter by exporting it, you select one of these options:

Export Coefficients, Objects, or System Objects to the Workspace.  You can save the filter as filter coefficients variables or filter System object™ variables.

To save the filter to the MATLAB workspace:

Export Filter Coefficients as a Text File.  To save your quantized filter as a text file, follow these steps:

Export Filter Coefficients as a MAT-File.  To save your quantized filter as a MAT-file, follow these steps:

Import XILINX .COE Files into Filter Designer

You can import XILINX coefficients (.coe) files into filter designer to create quantized filters directly using the imported filter coefficients.

To use the import file feature:

Filter Transformation Capabilities of Filter Designer

The toolbox provides functions for transforming filters between various forms. When you use filter designer with the toolbox installed, a side bar button and a menu bar option enable you to use the Transform Filter panel to transform filters as well as using the command line functions.

From the selection on the filter designer menu bar — Transformations — you can transform lowpass FIR and IIR filters to a variety of passband shapes.

You can convert your FIR filters from:

For IIR filters, you can convert from:

When you click the Transform Filter button, , on the side bar, the Transform Filter panel opens in filter designer, as shown here.

Your options for Original filter type refer to the type of your current filter to transform. If you select lowpass, you can transform your lowpass filter to another lowpass filter or to a highpass filter, or to numerous other filter formats, real and complex.

Original Filter Type

Select the magnitude response of the filter you are transforming from the list. Your selection changes the types of filters you can transform to. For example:

In the following table you see each available original filter type and all the types of filter to which you can transform your original.

Note also that the transform options change depending on whether your original filter is FIR or IIR. Starting from an FIR filter, you can transform to IIR or FIR forms. With an IIR original filter, you are limited to IIR target filters.

After selecting your response type, use Frequency point to transform to specify the magnitude response point in your original filter to transfer to your target filter. Your target filter inherits the performance features of your original filter, such as passband ripple, while changing to the new response form.

For more information about transforming filters, refer to Frequency Transformations for Real Filters and Frequency Transformations for Complex Filters.

Frequency Point to Transform

The frequency point you enter in this field identifies a magnitude response value (in dB) on the magnitude response curve.

When you enter frequency values in the Specify desired frequency location option, the frequency transformation tries to set the magnitude response of the transformed filter to the value identified by the frequency point you enter in this field.

While you can enter any location, generally you should specify a filter passband or stopband edge, or a value in the passband or stopband.

The Frequency point to transform sets the magnitude response at the values you enter in Specify desired frequency location. Specify a value that lies at either the edge of the stopband or the edge of the passband.

If, for example, you are creating a bandpass filter from a highpass filter, the transformation algorithm sets the magnitude response of the transformed filter at the Specify desired frequency location to be the same as the response at the Frequency point to transform value. Thus you get a bandpass filter whose response at the low and high frequency locations is the same. Notice that the passband between them is undefined. In the next two figures you see the original highpass filter and the transformed bandpass filter.

For more information about transforming filters, refer to Digital Frequency Transformations.

Transformed Filter Type

Select the magnitude response for the target filter from the list. The complete list of transformed filter types is:

Not all types of transformed filters are available for all filter types on the Original filter types list. You can transform bandpass filters only to bandpass filters. Or bandstop filters to bandstop filters. Or IIR filters to IIR filters.

For more information about transforming filters, refer to Frequency Transformations for Real Filters and Frequency Transformations for Complex Filters.

Specify Desired Frequency Location

The frequency point you enter in Frequency point to transform matched a magnitude response value. At each frequency you enter here, the transformation tries to make the magnitude response the same as the response identified by your Frequency point to transform value.

While you can enter any location, generally you should specify a filter passband or stopband edge, or a value in the passband or stopband.

For more information about transforming filters, refer to Digital Frequency Transformations.

Transform Filters.  To transform the magnitude response of your filter, use the Transform Filter option on the side bar.

Introduction

Not only can you design multirate filters from the MATLAB command prompt, filter designer provides the same design capability in a graphical user interface tool. By starting filter designer and switching to the multirate filter design mode you have access to all of the multirate design capabilities in the toolbox — decimators, interpolators, and fractional rate changing filters, among others.

Switch Filter Designer to Multirate Filter Design Mode

The multirate filter design mode in filter designer lets you specify and design a wide range of multirate filters, including decimators and interpolators.

With filter designer open, click Create a Multirate Filter, , on the side bar. You see filter designer switch to the design mode showing the multirate filter design options. Shown in the following figure is the default multirate design configuration that designs an interpolating filter with an interpolation factor of 2. The design uses the current FIR filter in filter designer.

When the current filter in filter designer is not an FIR filter, the multirate filter design panel removes the Use current FIR filter option and selects the Use a default Nyquist FIR filter option instead as the default setting.

Controls on the Multirate Design Panel

You see the options that allow you to design a variety of multirate filters. The Type option is your starting point. From this list you select the multirate filter to design. Based on your selection, other options change to provide the controls you need to specify your filter.

Notice the separate sections of the design panel. On the left is the filter type area where you choose the type of multirate filter to design and set the filter performance specifications.

In the center section filter designer provides choices that let you pick the filter design method to use.

The rightmost section offers options that control filter configuration when you select Cascaded-Integrator Comb (CIC) as the design method in the center section. Both the Decimator type and Interpolator type filters let you use the Cascaded-Integrator Comb (CIC) option to design multirate filters.

Here are all the options available when you switch to multirate filter design mode. Each option listed includes a brief description of what the option does when you use it.

To see the difference between hold interpolation and linear interpolation, the following figure presents a sine wave signal s1 in three forms:

You see in the bottom figure the sample and hold nature of hold interpolation, and the first-order linear interpolation applied by the linear interpolator.

Design a Fractional Rate Convertor.  To introduce the process you use to design a multirate filter in filter designer, this example uses the options to design a fractional rate convertor which uses 7/3 as the fractional rate. Begin the design by creating a default lowpass FIR filter in filter designer. You do not have to begin with this FIR filter, but the default filter works fine.

You can test the filter by exporting it to your workspace and using it to filter a signal. For information about exporting filters, refer to Import and Export Quantized Filters.

Design a CIC Decimator for 8 Bit Input/Output Data.  Another kind of filter you can design in filter designer is Cascaded-Integrator Comb (CIC) filters. Filter designer provides the options needed to configure your CIC to meet your needs.

Designing other multirate filters follows the same pattern.

To design other multirate filters, do one of the following depending on the filter to design:

Quantize Multirate Filters

After you design a multirate filter in filter designer, the quantization features enable you to convert your floating-point multirate filter to fixed-point arithmetic.

With your multirate filter as the current filter in filter designer, you can quantize your filter and use the quantization options to specify the fixed-point arithmetic the filter uses.

Quantize and Configure Multirate Filters.  Follow these steps to convert your multirate filter to fixed-point arithmetic and set the fixed-point options.

When you current filter is a CIC filter, the options on the Input/Output and Filter Internals panes change to provide specific features for CIC filters.

Input/Output.  The options that specify how your CIC filter uses input and output values are listed in the table below.

The available options change when you change the Filter precision setting. Moving from Full to Specify all adds increasing control by enabling more input and output word options.

Filter Internals.  With a CIC filter as your current filter, the Filter precision option on the Filter Internals pane includes modes for controlling the filter word and fraction lengths.

There are four usage modes for this (the same mode you select for the FilterInternals property in CIC filters at the MATLAB prompt).

Export Individual Phase Coefficients of a Polyphase Filter to the Workspace

After designing a polyphase filter in the filter designer app, you can obtain the individual phase coefficients of the filter by:

Export the Polyphase Filter to an Object.  To export a polyphase filter to an object in the MATLAB workspace, complete the following steps.

Create a Matrix of Coefficients Using the polyphase Method.  To create a matrix of the filter's coefficients, enter p=polyphase(Hm) at the command line. The polyphase method creates a matrix, p, of filter coefficients from the filter object, Hm. Each row of p consists of the coefficients of an individual phase subfilter. The first row contains to the coefficients of the first phase subfilter, the second row contains those of the second phase subfilter, and so on.

Introduction

After you design or import a filter in filter designer, the realize model feature lets you create a Simulink subsystem block that implements your filter. The generated filter subsystem block uses either digital filter blocks from the DSP System Toolbox library, or the Delay, Gain, and Sum blocks in Simulink. If you do not have a Fixed-Point Designer™ license, filter designer still realizes your model using blocks in fixed-point mode from Simulink, but you cannot run any model that includes your filter subsystem block in Simulink.

About the Realize Model Panel in Filter Designer

To access to the Realize Model panel and the options for realizing your quantized filter as a Simulink subsystem block, switch filter designer to realize model mode by clicking on the sidebar.

The following panel shows the options for configuring how filter designer implements your filter as a Simulink block.

For information on these parameters, see the descriptions on the Filter Realization Wizard block reference page.

Realize a Filter Using Filter Designer.  After your quantized filter in filter designer is performing the way you want, with your desired phase and magnitude response, and with the right coefficients and form, follow these steps to realize your filter as a subsystem that you can use in a Simulink model.

If you double-click the filter block subsystem created by filter designer, you see the filter implementation in Simulink model form. Depending on the options you chose when you realized your filter, and the filter you started with, you might see one or more sections, or different architectures based on the form of your quantized filter. From this point on, the subsystem filter block acts like any other block that you use in Simulink models.