Мне нужно применить фильтр Баттерворта. Чтобы доказать мою частоту среза, я хочу построить график зависимости остатков от частоты среза, как показано на рисунке справа:

Остатки вычисляются с использованием выражения, показанного на рисунке слева.

Я хочу применить низкочастотный фильтр Баттерворта второго порядка. Моя частота дискретизации составляет 40 Гц.

С помощьюhelp butter гласит:

«Частота среза Wn должна составлять 0,0 <Wn <1,0, при этом 1,0 соответствует половине частоты дискретизации».

Это мой код, гдеx это нефильтрованные данные:

x = 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.060092500000;393.418588700000;394.132615800000;394.432453800000;398.324667600000;397.096586200000;398.005721400000;400.474732000000;400.328915300000;401.058421000000;403.238428000000;402.724730000000;403.253563800000;404.687953000000;405.079930400000;405.219330800000;407.047728400000;407.595529300000;408.057711800000;408.539252700000;409.836387000000;410.123266400000;410.313569400000;412.099500000000;412.793454600000;413.372957300000;415.066474200000;413.971619400000;414.254327400000;415.198047500000;416.134740700000;417.933600600000;417.211507700000;417.097779400000;417.708317200000;414.171904400000;412.326958700000;410.969281800000;403.879401900000;399.416247400000;393.297210900000;389.540637800000;384.152425200000;376.404144800000;372.813625800000;366.430311000000;361.093876700000;358.405677900000;358.336124000000;358.933857600000;363.550827300000;368.513013500000;373.555796400000;377.399377100000;382.541254000000;385.282657700000;389.342241000000;390.319845400000;390.834423800000;390.247456200000;392.237231500000;393.850930200000;398.146367200000;400.318802200000;404.104563600000;404.659164900000;];
wc = 0.001:0.001:1 % <----- !!!
R = zeros(1, length(wc)-1);
for nn = 1:length(wc)-1
    [B,A] = butter(2,wc(nn));
    xprime = filtfilt(B,A,x);
    R(1,nn) = sqrt(1/length(x)*(sum(abs(x-xprime).^2)))
end         
plot(wc(1:end-1)*20,R) % <------ !!!!

И я получил это:

Но это не кажется мне правильным. Что я делаю неправильно?