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I have a 10 bit ADC sample stream in which I would like to apply a digital band pass filter. Is there a theoretical filter tap count that would define the threshold of "usefulness"?

I guess my thought process is: There are only 10 bits, so at some point (via increasing the tap count) the attenuation will be so great that even a maximum amplitude frequency component will get attenuated down to a fraction of a bit, and rounded down to 0. At that point, the effects of additional taps could not be seen.

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Since you can widen your bit width with each operation, no, there's no such maximum useful width.

Take GPS receivers as an example: many of them citation needed use 2 bit ADCs and yet are useful, because the signal, already hidden in noise before it reaches the ADC, only gets "visible" by massive processing gain.

A typical step with massive processing gain would be a very sharp digital filter. Those can get very long.

There's a lot of experienced audio and video folks on here. They can tell you much more about the astronomical lengths high-quality filters can get.

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No. Although one may argue if, as you say, there is any benefit of attenuating beyond, say, 70 dB, there are special cases as Marcus point out where this doesn't hold. Another such case is if you are oversampling the signal. In addition, making an arbitrary narrow transition band will increase the filter order arbitrarily.

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