Design low pass filter with a given transfer function

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Giovanni Lo Bocchiaro
Giovanni Lo Bocchiaro 2019 年 5 月 24 日
I must design a low-pass filter with a given transfer function in z-domain:
H(z) = (1-z^(-6))^2 / (1-z^(-1))^2
Considering the x signal (1x2000) I want to filter, i wrote
N = 2000;
h1 = zeros(1,N);
%
% a. Low-Pass Filter
for i = 1:N
if (i == 1)
h1(1) = 1;
a1(1) = 1;
b1(1) = 1;
else
if (i == 2)
h1(2) = 1/(1-2*x(1));
b1(2) = 1;
a1(2) = 1-2*x(1);
else
if ((i == 3) || (i == 4) || (i == 5) || (i == 6))
h1(i) = 1/(1+x(i-2)-2*(x(i-1)));
b1(i) = 1;
a1(i) = (1+x(i-2)-2*(x(i-1)));
else
if ((i == 7) || (i == 8) || (i == 9) || (i == 10) || (i == 11) || (i == 12))
h1(i) = ((1-2*x(i-6)))/(1+(x(i-2))-2*(x(i-1)));
b1(i) = (1-2*x(i-6));
a1(i) = (1+(x(i-2))-2*(x(i-1)));
else
h1(i) = ((1+(x(i-12))-2*(x(i-6))))/(1+(x(i-2))-2*x(i-1));
b1(i) = ((1+(x(i-12))-2*(x(i-6))));
a1(i) = (1+(x(i-2))-2*x(i-1));
end
end
end
end
end
figure,
freqz(b1,a1,512,fc);
y = filter(b1,a1,x);
Is it correct? I don't think so because the plot it is a mess and definitively not a low-pass! What is it wrong?

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