iir filter saturation problems

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nxp nxp
nxp nxp on 21 Sep 2022
Commented: Chunru on 21 Sep 2022
I want to implement IIR filter without MATLAB functions. I get the coefficients as follows (Fs = 1000 , BPF 5-15Hz)
f1=5;
f2=15;
Wn=[f1 f2]*2/fs;
N = 3;
[b,a] = butter(N,Wn);
b = flipud(b')
a = -flipud(a')
b coff:
1.0e-04 *
-0.2915
0
0.8744
0
-0.8744
0
0.2915
a coff:
-0.8819
5.3942
-13.7568
18.7244
-14.3455
5.8657
-1.0000
And I have written the filter code as below, but the output goes to infinity.
for i = 7 : N
BPF(i) = 0.0001*(-0.2915*X(i) +0.8744* X(i-2) - 0.8744* X(i-4) + 0.2915* X(i-6))...
+(-0.8819*BPF(i-1)+5.3942*BPF(i-2)-13.7568* BPF(i-3)+18.7244*BPF(i-4)-14.3455*BPF(i-5)+5.8657*BPF(i-6));
end

Answers (1)

Chunru
Chunru on 21 Sep 2022
It seems that your implementation of filter is not correct and hencie make the iir filter not stable:
for i = 7 : N
BPF(i) = 0.0001*(-0.2915*X(i) +0.8744* X(i-2) - 0.8744* X(i-4) + 0.2915* X(i-6))...
+(-0.8819*BPF(i-1)+5.3942*BPF(i-2)-13.7568* BPF(i-3)+18.7244*BPF(i-4)-14.3455*BPF(i-5)+5.8657*BPF(i-6));
end
Replace above with
BPF = filter(b, a, X)
  2 Comments
nxp nxp
nxp nxp on 21 Sep 2022
its right.But why it is not stable? for initial value of output? I want to implement it with C
Chunru
Chunru on 21 Sep 2022
For iir filter, the poles of transfer function must be within unit circle to be stable.
Your filter formula is implemting a different filter from "filter(b, a, x)" and it somehow not stable. Check out your implementation according the the IIR filter formula.

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