MATLAB: What does the scale setting exactly signify in the “Reordering and Scaling of Second-Order Sections” window of FDATool

Filter Design Toolboxnonenormalizeunit

I would like to get some clarification on the Scale settings in the "Reordering and Scaling of Second-Order Sections" window of FDATool. I read the documentation, but the documentation is not clear on some of the terms.

For the Numerator Constraint, what is the difference between "Normalize", "Unit" and "None"?

For the Scale Value Constraint, what is the difference between "Unit" and "None"?

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The current documentation on the Reordering and Scaling of Second-Order Sections options is incomplete in the manual. Here is additional information on these options:

For the Numerator Constraint:

"Normalize" - the maximum absolute value of the numerator is forced to be equal to the "Maximum Numerator" value. For all others constraints "Maximum Numerator" is just an upper limit over which coefficients are clipped.

"Unit" - the leading coefficient of each numerator is forced to 1.

"None" - no constraint on the numerator coefficients other than being lower than the "Maximum Numerator" value.

 For the Scale Value Constraint:

"Unit" - all scale values (except the last one) are forced to 1. (Notice that the first scale value of df2sos and df1tsos can not be constrained either)

"None" - scale values can take any value up to the "Max Scale Value".

Related Solutions

MATLAB: Numerator and denominator coefficients from designfilt function

The type of coefficients you encounter are called Second order section coefficients. Second-order section coefficients, specified as a matrix. sos is a K-by-6 matrix, where the number of sections, K, must be greater than or equal to 2. If the number of sections is less than 2, the function treats the input as a numerator vector. Each row of sos corresponds to the coefficients of a second-order (biquad) filter. The ith row of sos corresponds to [bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)].

%Create a filter object using designfilt
filterObj = designfilt('lowpassiir', 'PassbandFrequency', .45, 'StopbandFrequency', .55, 'PassbandRipple', 1, 'StopbandAttenuation', 60);
%Convert the second order section coefficients to tranfer function format
[b,a] = sos2tf(filterObj.Coefficients);
%Here b is the numerator and a is the denominator

MATLAB: FDA Tool

The SOS Matrix is an M x 6 matrix that provides the unscaled coefficients for the M second-order sections that, when cascaded, implement the filter. The Scale values option outputs an M x 1 column vector G, each element of which is essentially a multiplicative gain factor that you can use simply to scale each second-order section so that the overall filter is referenced to 0 dB. So G does not affect the shape of the output waveform or spectrum, but it does affect the scale or level of the output or spectrum.

Does that make sense?

Rick

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MATLAB: Numerator and denominator coefficients from designfilt function

MATLAB: FDA Tool

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