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?