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I believe a related question is asked here, but my question deals more with what filter is realized if one fails to consider design parameters relative to sampling rate.

In designing an IIR filter we really want our roll-off frequency to be significantly less than the Nyquist frequency; it makes sense to do so. But what results if the designer fails to do so? Instability in the filter? A sort of aliasing of the rolloff frequency (not the signal)? Or are both possible?

For example I design a first order low pass filter that samples and computes output at 1000 Hz (Nyquist = 500 Hz), but I pick my filter pole at 1200 Hz!

Simulation shows that the resulting filter is stable , but of course the cutoff is much lower than expected.

It appears, at least for this example that it is not an aliasing of signal, but rather an aliasing of the design. Is there a better term than aliasing to use in this case?

Is there something more general to be said about improper design choice. In the case of a second order filter can the improper choice of bandwidth/sampling lead to instability in an IIR? Or rather the same result as the first order example?

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  • $\begingroup$ What method are you using to design IIR filters? Bilinear transform, impulse response invariance, or some other method? $\endgroup$
    – Juancho
    Commented Jan 24, 2017 at 19:38
  • $\begingroup$ I purposely didn't mention method to keep the question general, but for the example and my simple I used a backward rectangular approximation for integration for discretation $\endgroup$
    – docscience
    Commented Jan 24, 2017 at 19:50
  • $\begingroup$ well, doc, it does matter whether it's bilinear transform or impulse invariant. the former doesn't alias any features in the frequency response (but there is frequency warping, which can be compensated for each degree of freedom in the frequency specification) and the latter does alias features in the frequency response. both $s \to z$ mappings always map a stable $s$-plane filter to a stable $z$-plane filter. $\endgroup$
    – robert bristow-johnson
    Commented Jan 26, 2017 at 4:59
  • $\begingroup$ @robertbristow-johnson since my post I've given more thought myself and you are right, choice of mapping does matter. If the poles are complex and you map using a forward rectangular approximation, indeed the poles can shift outside the unit circle. I'm still not sure, but I don't think aliasing ever occurs. I believe any sense of filtering just ceases when the poles far exceed sampling frequency. $\endgroup$
    – docscience
    Commented Jan 26, 2017 at 5:53
  • $\begingroup$ i've been doing DSP for 35 years and i even know a thing or two about how filters are designed and how analog filters might be converted to digital. i have never heard of a "forward rectangular approximation". is that something you Control Systems folks use? would you tell me what it is? $\endgroup$
    – robert bristow-johnson
    Commented Jan 26, 2017 at 6:02

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