第１種チェビシェフフィルタの伝達関数の分母多項式の係数の計算

clear; close all;

s = tf('s');

xis = [0.1 0.5 1];
es = sqrt(10.^(xis/10)-1);

e = es(1);
tmp = sqrt(1+e^(-2))+e^(-1);


for n = 1:10
    D = 1;
    for k=1:n
        sinhv = 1/2*(tmp^(1/n)-tmp^(-1/n));
        coshv = 1/2*(tmp^(1/n)+tmp^(-1/n));
        sigma_k = -sin((2*k-1)/(2*n)*pi)*sinhv;
        omega_k = cos((2*k-1)/(2*n)*pi)*coshv;
        sk = sigma_k + i*omega_k;
        D = D*(s-sk);
    end
    coef(D)
end


function n = coef(D)
[n,d] = tfdata(D);
n = cell2mat(n);
n = n(2:end);
n = real(n);
end

実行結果

>> cheb2
ans =
    6.5522
ans =
    2.3724    3.3140
ans =
    1.9388    2.6295    1.6381
ans =
    1.8038    2.6268    2.0255    0.8285
ans =
    1.7440    2.7707    2.3970    1.4356    0.4095
ans =
    1.7122    2.9658    2.7791    2.0478    0.9018    0.2071
ans =
    1.6932    3.1835    3.1692    2.7051    1.4829    0.5618    0.1024
ans =
    1.6810    3.4129    3.5648    3.4185    2.1592    1.0666    0.3264    0.0518
ans =
  Columns 1 through 8
    1.6727    3.6490    3.9638    4.1916    2.9339    1.7341    0.6942    0.1918
  Column 9
    0.0256
ans =
  Columns 1 through 8
    1.6668    3.8891    4.3654    5.0262    3.8085    2.5790    1.2297    0.4572
  Columns 9 through 10
    0.1070    0.0129
>>