Learn more about Filter Design Toolbox

Reordering the Sections of Second-Order Section Filters

On this page…
Switching FDATool to Reorder Filters

Switching FDATool to Reorder Filters

FDATool design 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 FDATool, either one you designed in the tool, or one you imported, FDATool provides the capability to change the order of the sections that compose the filter. Any SOS filter in FDATool 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 FDATool.

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

Controls on the Reordering and Scaling of Second-Order Sections dialog box

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 Scaling 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.

Control Option	Description
Auto	Reorders the filter sections to minimize the output noise power of the filter. Note that different ordering applies to each specification type, such as lowpass or highpass. Automatic ordering adapts to the specification type of your filter.
None	Does no reordering on your filter. Selecting None lets you scale your filter without applying reordering at the same time. When you access this dialog box with a current filter, this is the default setting — no reordering is applied.
Least selective section to most selective section	Rearranges the filter sections so the least restrictive (lowest Q) section is the first section and the most restrictive (highest Q) section is the last section.
Most selective section to least selective section	Rearranges the filter sections so the most restrictive (highest Q) section is the first section and the least restrictive (lowest Q) section is the last section.
Custom reordering	Lets you specify the section ordering to use by enabling the Numerator Order and Denominator Order options
Numerator Order	Specify new ordering for the sections of your SOS filter. Enter a vector of the indices of the sections in the order in which to rearrange them. For example, a filter with five sections has indices 1, 2, 3, 4, and 5. To switch the second and fourth sections, the vector would be [1,4,3,2,5].
Use Numerator Order	Rearranges the denominators in the order assigned to the numerators.
Specify	Lets you specify the order of the denominators, rather than using the numerator order. Enter a vector of the indices of the sections to specify the order of the denominators to use. For example, a filter with five sections has indices 1, 2, 3, 4, and 5. To switch the second and fourth sections, the vector would be [1,4,3,2,5].
Use Numerator Order	Reorders the scale values according to the order of the numerators.
Specify	Lets you specify the order of the scale values, rather than using the numerator order. Enter a vector of the indices of the sections to specify the order of the denominators to use. For example, a filter with five sections has indices 1, 2, 3, 4, and 5. To switch the second and fourth sections, the vector would be [1,4,3,2,5].
Revert to Original Filter	Returns your filter to the original section ordering. Being able to revert to your original filter makes comparing the results of changing the order of the sections easier to assess.

Example — Reorder an SOS Filter

With FDATool open and 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 FDATool from the command prompt.

1. Enter fdatool at the command prompt to launch FDATool.

2. Design a lowpass Butterworth filter with order 10 and the default frequency specifications by entering the following settings:

   • Under Response Type select Lowpass.

   • Under Design Method, select IIR and Butterworth from the list.

   • Specify the order equal to 10 in Specify order under Filter Order.

   • Keep the default Fs and Fc values in Frequency Specifications.

3. Click Design Filter.

   FDATool design the Butterworth filter and returns your filter as a Direct-Form II filter implemented with second-order sections. You see the specifications in the Current Filter Information area.

   With the second-order filter in FDATool, reordering the filter uses the Reordering and Scaling of Second-Order Sections feature in FDATool (also available in Filter Visualization Tool, fvtool).

4. To reorder your filter, select Edit > Reorder and Scale Second-Order Sections from the FDATool menus. FDATool opens the following dialog box that controls reordering of the sections of your filter.

   

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

Use Least Selective to Most Selective Section Reordering

To let FDATool 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.

1. In Reordering, select Least selective section to most selective section.

2. To prevent filter scaling at the same time, clear Scale in Scaling.

3. In FDATool, select View > SOS View from the menu bar so you see the sections of your filter displayed in FDATool.

4. In the SOS View dialog box, select Individual sections. Making this choice configures FDATool to show the magnitude response curves for each section of your filter in the analysis area.

5. Back in the Reordering and Scaling of Second-Order Sections dialog box, click Apply to reorder your filter according to the Qs of the filter sections, and keep the dialog box open. In response, FDATool presents the responses for each filter section (there should be five sections) in the analysis area.

   In the next two figures you can compare the ordering of the sections of your filter. In the first figure, your original filter sections appear. In the second figure, the sections have been rearranged from least selective to most selective.

   

   

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.

Back to Top

Scaling Second-Order Section Filters

Viewing SOS Filter Sections

© 1984-2009- The MathWorks, Inc.    -   Site Help   -   Patents   -   Trademarks   -   Privacy Policy   -   Preventing Piracy   -   RSS