The Nyquist criterion dictates that all signals must be bandlimited to less than half the sampling rate of the sampling system. Many signals already have a limited spectrum, so this is not a problem. However, for broad spectrum signals, an analog lowpass filter must be placed before the data acquisition system. The minimum attenuation of this filter at the aliasing frequency should be at least: where B is the number of bits of the ADC. This formula is derived from the fact that there is a minimum noise level inherent in the sampling process and there is no need to attenuate the sensor signal more than to below this noise level.

- 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. - 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.
- Amplitude Distortion: By definition, the filter will modify the frequency structure of the sensor signal which is usually not desired

- Increase the sampling rate of the ADC. This allows the antialiasing filter to have a
higher cutoff frequency and still eliminate aliasing. This enables the following:
- The filter rolloff can be more shallow - allowing a better time response
- The frequency response of the filter does not attenuate the lower sensor frequencies of interest
- Phase distortion is strongest around the cutoff frequency of the filter so if this is pushed higher, it will not affect the sensor frequencies this cutoff

- Have linear phase filters. This, of course, will reduce the phase distortion problems.

Thu Oct 17 16:32:33 PDT 1996