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

Parameter | Description and Valid Value |
|---|---|
Scale | Apply any scaling options to the filter. Select this when you are reordering your SOS filter and you want to scale it at the same time. Or when you are scaling your filter, with or without reordering. Scaling is disabled by default. |
No Overflow — High SNR slider | Lets you set whether scaling favors reducing arithmetic overflow in the filter or maximizing the signal-to-noise ratio (SNR)) at the filter output. Moving the slider to the right increases the emphasis on SNR at the expense of possible overflows. The markings indicate the P-norm applied to achieve the desired result in SNR or overflow protection. For more information about the P-norm settings, refer to norm for details. |
Maximum Numerator | Maximum allowed value for numerator coefficients after scaling. |
Numerator Constraint | Specifies whether and how to constrain numerator coefficient values. Options are none, normalize, power of 2, and unit. Choosing none lets the scaling use any scale value for the numerators by removing any constraints on the numerators, except that the coefficients will be clipped if they exceed the Maximum Numerator. With Normalize the maximum absolute value of the numerator is forced to equal the Maximum Numerator value (for all other constraints, the Maximum Numerator is only an upper limit, above which coefficients will be clipped). The power of 2 option forces scaling to use numerator values that are powers of 2, such as 2 or 0.5. With unit, the leading coefficient of each numerator is forced to a value of 1. |
Overflow Mode | Sets the way the filter handles arithmetic overflow situations during scaling. Choose from either saturate (limit the output to the largest positive or negative representable value) or wrap (set overflowing values to the nearest representable value using modular arithmetic. |
Scale Value Constraint | Specify whether to constrain the filter scale values, and how to constrain them. Valid options are unit, power of 2, and none. Choosing unit for the constraint disables the Max. Scale Value setting and forces scale values to equal 1. Power of 2 constrains the scale values to be powers of 2, such as 2 or 0.5, while none removes any constraint on the scale values, except that they cannot exceed the Max. Scale Value. |
Max. Scale Value | Sets the maximum allowed scale values. SOS filter scaling applies the Max. Scale Value limit only when you set Scale Value Constraint to a value other than unit (the default setting). Setting a maximum scale value removes any other limits on the scale values. |
Revert to Original Filter | Returns your filter to the original scaling. Being able to revert to your original filter makes it easier to assess the results of scaling your filter. |
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.
Start the process by designing a lowpass elliptical filter in FDATool.
In Design Method, select IIR and Elliptic from the IIR design methods list.
Switch the frequency units by choosing Normalized(0 to 1) from the Units list.
To set the passband specifications, enter 0.45 for wpass and 0.55 for wstop. Finally, in Magnitude Specifications, set Astop to 60.
Click Design Filter to design the filter.
After FDATool finishes designing the filter, you see the following plot and settings in the tool.

You kept the Options setting for Match exactly as both, meaning the filter design matches the specification for the passband and the stopband.
To switch to scaling the filter, select Edit > Reorder and Scale Second-Order Sections from the menu bar.
Your selection opens the Reordering and Scaling Second-Order Sections dialog box shown here.

To see the filter coefficients, return to FDATool and select Filter Coefficients from the Analysis menu. FDATool displays the coefficients and scale values in FDATool.

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.
Return to the Reordering and Scaling Second-Order Sections dialog box and select None for Reordering in the left pane. This prevents FDATool from reordering the filter sections when you rescale the filter.
Move the No Overflow—High SNR slider from No Overflow to High SNR.
Click Apply to scale the filter and leave the dialog box open.
After a few moments, FDATool updates the coefficients displayed so you see the new scaling, as shown in the following figure.

All of the scale factors are now 1, and the SOS matrix of coefficients shows that none of the numerator coefficients are 1 and the first denominator coefficient of each section is 1.
Click Revert to Original Filter to restore the filter to the original settings for scaling and coefficients.
![]() | Analyzing Filters with a Noise-Based Method | Reordering the Sections of Second-Order Section Filters | ![]() |

Learn how to apply early verification to your development process through these technical resources.
How much time do you spend on testing to ensure implementation meets system-level requirements?
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