As we reach the end of this chapter on poles and feedback filtering, we might be inclined to conclude that all is well if poles are outside the unit circle and that they may even come close to the circle. Further, if we accept anticausal filtering, poles can be inside the unit circle as well.
Reality is more difficult.
Big trouble can arise from just a modest clustering of poles at a moderate distance from the unit circle. A pathological failure when poles cluster too much. This situation requires more than single-word precision. The spectrum should look like the spectrum in Figure 8 multiplied by itself about six or seven times, once for each pole. The effect of such repetitive multiplication is to make the small spectral values become very small.