tf2sos of iirnotch giving different results

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Daoyuan 2014-12-11

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https://ww2.mathworks.cn/matlabcentral/answers/166350-tf2sos-of-iirnotch-giving-different-results

评论： Daoyuan 2014-12-15

Hi,

I am trying to use iirnotch() for filtering, I noticed that if I ran the coefficients from iirnotch (2nd order) through tf2sos (still comes out to be the exact same numbers), the frequency response of (b,a) and (sos) showed in freqz() or fvtool() gives very different results.

eg: [b,a] = iirnotch(wo,bw); [sos1] = tf2sos(b,a); freqz (b, a, Fs); freqz (sos, Fs);

I was wondering how come there is a difference?

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Answer 1

Star Strider 2014-12-11

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You didn’t post the details of your code so I can only provide a general reply. As the documentation states, the second-order-section (‘sos’) implementation of a filter characteristically produces the most stable version of the filter. The transfer function (‘tf’) is usually less stable. Therefore, the plotted filter passband-stopband characteristics may be different between the two implementations. (I convert to and use the ‘sos’ implementation whenever I design a filter.)

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Daoyuan 2014-12-12

Thanks for the answer, my code is similar to the eg I gave, so for example, I was testing the notch filter for power line interference.

%60 Hz noise, at 300Hz sampling frequency

wo = 60/(300/2); bw = wo/35;

[b,a] = iirnotch(wo,bw);

fvtool(b,a);

sos = tf2sos(b,a);

fvtool(sos);

From the result of this code, the first and second graph looks completely different, the first graph having around -80dB notch with a flat band everywhere else, and the second has a wide notch of only -40dB, and with a non-flatband after the notch. However I am confused because if you look at the values in b & a versus the values in SOS, they are the exact same values:

sos = 0.98236277 -0.607133581 0.98236277 1 -0.607133581 0.96472554

b = 0.98236277 -0.607133581 0.98236277

a = 1 -0.607133581 0.96472554

However, the graph in the fvtool or freqz shows very different results. I was wondering since the notch provides a second order iir filter, and the sos is a second order iir filter, both with the same values, how are they producing different results. To my knowledge I thought the sos should produce the same results as the original iir filter if both are second order, since the tf2sos converts high order into cascaded second order filters.

Star Strider 2014-12-12

Your previous Comment seems to have solved the problem. Still, there seems something anomalous about the results you’re getting with the SOS implementation. Something is wrong somewhere, and it isn’t in your code.

I suggest you mention your findings to The MathWorks in a bug report. Copy and paste the URL for your Question here to your bug report so you don’t have to repeat everything.

Daoyuan 2014-12-15

OK, thanks for the advice, I will try to send a bug report.

=D

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