What criteria should be used to safely decide if it is an IIR filter or FIR filter from a difference equation? FIR filter are always stable, meaning all poles are inside the unit circle AND have pole-zero cancellations i.e have equal number of poles and zeros at the same point in the z-plane. IIR filters are conditionally stable, i.e always have poles on/outside the unit circle. Is this good enough to distinguish from the difference equation? what other criteria should be considered?
PS: Please don't say IIR filters have recursive difference equations, and FIR doesn't. It is not true.