BUTTER function returning slightly different results for Signal Processing Toolbox in R2020b and R2021a on same computer (Win10)

[numerator, denominator] = butter(9, 0.5 / (100/2), 'high')

The returned numerator coefficients are slightly different for R2021a when compared to output from R2020b on the same Win10 computer. The difference is quite small (on the order of 1E-13) but is resulting in some analysis differences. I get identical coefficient values for R2020b, R2020a or R2019a.

I tried using a technique outlined in an older thread where user appeared to run into a similar issue but differences persist ( https://www.mathworks.com/matlabcentral/answers/98640-why-does-the-butter-function-return-different-results-for-signal-processing-toolbox-4-3-and-5-0 ).

Matlab release notes don't indicate something was changed in BUTTER function for R2021a version.

[Bjorn Gustavsson]

In my matlab-version butter is a plain .m-file - if that's the case in your matlab-version you might be able to simply run a diff (in the editor (of your choise))...

[JS]

Thanks for the suggestion (I had mistakenly assumed they would be p-files). There appear to a number of differences in how numerator and denominator coefficients are calculated.

R2021a

p = eig(a);

[z,k] = buttzeros(btype,n1,Wn1,analog,p+0i);

den = real(poly(p));

num = [zeros(1,length(p)-length(z),'like',den) k*real(poly(z))];

R2019a:

den = poly(a);

num = buttnum(btype,n,Wn,Bw,analog,den);

"buttzeros.m" in R2021a and "buttnum.m" in R2019b appear to serve similar purpose but there are differences (and since support functions include .p-files, in-depth debugging is not possible).

[Cris LaPierre]

I suggest contacting support. If you receive an answer to your question, consider posting here.

Answer 1

[Jan]

You can compare both results with this cheap implementation of a high pass Butterworth filter:

format long g
[num, den]   = butter(9, 0.5 / (100/2), 'high');
[num2, den2] = cheapButterHigh(9, 0.5 / (100/2));
[num.' - num2.' , den.' - den2.']

ans = 10×2

1.0e+00 * -4.44089209850063e-16 0 3.5527136788005e-15 0 -1.4210854715202e-14 0 2.8421709430404e-14 2.8421709430404e-14 -5.6843418860808e-14 -4.2632564145606e-14 5.6843418860808e-14 4.2632564145606e-14 -2.8421709430404e-14 -4.2632564145606e-14 1.4210854715202e-14 2.1316282072803e-14 -3.5527136788005e-15 -5.32907051820075e-15 4.44089209850063e-16 6.66133814775094e-16

function [num, den] = cheapButterHigh(n, W)
% A simple high pass Butterworth implementation.
% Jan, Heidelberg, CC BY-SA 3.0
V  = tan(W * 1.5707963267948966);  % pi/2
Q  = exp((1.5707963267948966i / n) * ((2 + n - 1):2:(3 * n - 1)));

Sg = 1 ./ prod(-Q);
Sp = V ./ Q;

% Bilinear transform:
P = (1 + Sp) ./ (1 - Sp);
G = real(Sg / prod(1 - Sp));
Z = ones(length(Q), 1);

% From Zeros, Poles and Gain to B (numerator) and A (denominator):
num = G * real(poly(Z));
den = real(poly(P));
end

For large n this implementation is assumed to be less stable than Matlab's version, but I need it for n < 12 only.

Although this cheaper version is 10 times faster, it is not thought to save run time: Usually a program does not need tenthousands of different filter parameters.

[JS]

Thank you for posting this. Your implementation is giving consistent coefficient values for R2021a and previous versions which will be useful for running comparisons. I reached out to Matlab in the meantime to get a better understanding of implemented changes for R2021a (and newer versions) and will post update when available.

[Chris Heyman]

Hi JS,

Did you ever recieve a response from Matlab about this?

Thanks

-C