Problems with the Anti-aliasing Filter:

1. Time Response: In designing an anti-aliasing filter, there is a temptation to have it's attenuation roll-off extremely quickly. The way to achieve this is to increase the order of the filter (see the previous discussion of filter order). A so-called brick-wall filter (one with infinitely high order), however, causes a sinc function time response that decays proportionally to 1/t. What this means is that an extremely high order filter that eliminates all signals above the cutoff frequency will cause signals that change rapidly to ring on for a long time. A very undesirable effect.
2. Phase Distortion / Time delay: Most analog filters have a non-linear phase response. This a problem since non-linear phase causes an unequal time (group) delay as a function of frequency. The higher frequency signals will arrive later than low frequency signals. This can especially be a problem when multiple sensor outputs are compared such as when using a microphone array.
3. Amplitude Distortion: By definition, the filter will modify the frequency structure of the sensor signal which is usually not desired