Hi all Is there a generally accepted rule as to which order to perform filtering in?

for example if I have three iir filters, a low pass filter a notch and a high pass filter, which sequence would it be best to perform these in? or does it not make any difference at all?

cheers, Graham.

  • $\begingroup$ So the order should not make a difference? I was finding that if I high pass filtered first, then there was a dc offset on the output but if I high pass filtered last the dc offset was gone. $\endgroup$ – SlyRaccoon Feb 25 '15 at 9:34

Theoretically (with infinite precision arithmetic) order of LTI filters does not matter. If any of the filters is not LTI then order will be important.

Plus, for finite precision arithmetic one should also take care of numerical error build up and potential instability issues especially with IIR filters where pole locations may become critical

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    $\begingroup$ +1, but I would add that order matters when you are using filters that change the sample rate. $\endgroup$ – Jim Clay Feb 19 '15 at 13:07
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    $\begingroup$ @Jim Clay: thank you, and I guess those sample rate converting filters are Linear but Time Varying systems hence they are not LTI. Therefore their order will matter as expected. $\endgroup$ – Fat32 Feb 19 '15 at 13:23
  • $\begingroup$ No, I believe that resampling FIR filters are LTI, in that they obey superposition and their characteristics do not change over time. $\endgroup$ – Jim Clay Feb 19 '15 at 13:46
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    $\begingroup$ @JimClay: you are right their charactheristics do not change over time but the following derivation shows that they are time-varying: consider y[n]=x[Mn], let x2[n]=x[n-d], then y2[n]=x2[Mn]=x[Mn-d], then y2[n] is not equal to y[n-d]=x[M(n-d)]=x[Mn-Md], therefore a compressor (downsampler) is a Time Varying system... $\endgroup$ – Fat32 Feb 19 '15 at 16:32
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    $\begingroup$ Yes, you're right. $\endgroup$ – Jim Clay Feb 19 '15 at 16:34

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