numerator and denominator coefficients from designfilt function

I am designing an lowpass IIR filter using designfilt function. I found coefficients for the filter which is 9x6 Double. Now, how can I find numerator and denominator from this?

Answer 1

[Nipun Katyal]

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

[Rohit Mallampati]

Thanks Nipun

[John Gauci]

This does not always work. For example:

filterObj2 = designfilt('lowpassiir', 'PassbandFrequency', 0.02, 'StopbandFrequency', 0.04, 'PassbandRipple', 1, 'StopbandAttenuation', 60);
fvtool(filterObj2);
[b,a] = sos2tf(filterObj2.Coefficients);
fvtool(b,a);

shows two very different filter reponses, the second being drastically wrong and which gets worse the closer the stop band gets to the pass band.

Is there another way of getting the coefficients from designfilt?

Answer 2

[Peter Bode]

Do Mathworks stiil support the legacy filter design functions which have been proven useful for decades?