Bandwidth requirement to pass fast rising digital signals

How wide must the bandwidth be to pass a fast rising digital pulse so that at the output it can still be recognized as a pulse and detected? A common enough question. However sometimes the answer is not so obvious. Common wisdom says a minimum 3dB point of the filter or medium through which the pulse has to transition must be at least 1/pi*tr where tr is the risetime and pi is 3.1415 etc. Upon simulation using a simple RC filter, the result is: (a) The rule is correct. (b) The pulse width and period must be such as to accomodate the rise and fall time of the pulse. (c) The bandwidth may be narrower if the detection threshold can be set higher. (d) If the detection threshold is low then detection errors may occur if the above rules are disobeyed!