Dave Tweed wrote: > OK, so you're saying that if two filters have the same response at > Fs/2, they have the same "random noise" attenuation? At least I now > know what you mean, but I don't think that's actually a useful > criterion in real- world applications. It's certainly far from perfect, but it's not totally useless either. Ther= e are a lot of things you can do with low pass filters, but I mentioned this in the context of continually measuring a anlog signal such as you might do in a PIC for a control applications. In this application, there are two primary things you want to know about a filter applied after the A/D readings and before the rest of the system uses the current value: 1 - How much can it reduce the noise? Presumably this is the reason for inserting a filter as I described above. If you weren't concerned about noise, you'd probably use the A/D readings directly. (You might also be doing additional anti-aliasing to support later decimation, but that's a advanced topic I think better left out here). 2 - How much is it going to slow down my signal? You'd like the filter not to delay the real signal at all, but it's not going to reduce noise without some delay. So another question might be how much delay do I get stuck wit= h for various noise reduction levels? Ideally you want something that squashes all the noise but doesn't delay th= e signal at all. Unfortunately, that's a free lunch you don't get to eat, so you have to consider the real tradeoffs. That means quantifying "delay" an= d "noise reduction" somehow. Each have various metrics. For delay, the 90% or 95% or (2**N - 1)/(2**N) step response are usually good things to look at. A metric for "noise reduction" is not so easy because it's hard to define what exactly you mean by noise in your particular situation. This is where I used the loose term "random noise". As you said that really turned out t= o be a signal with frequency Fs/2. Obviously all noise doesn't come in at Fs/2, but the attenuation there can give you at least some idea what the filter will do with unspecified "noise" on your ideal A/D readings. Of course no frequency based filter is going to do anything with noise within the valid frequency range of the real signal. Another noise metric of a filter could be the maximum amplitude of the discrete unit impulse response. That is FF for a single pole filter, but more than the product of all the FFs of a multi-pole filter. Real "noise squashing" (whatever that really means) of a multi-pole filter is probably somewhere between these two metrics. It gets complicated if you want to do the analisys at this detail. My original point is still true however. That was that you get better tradeoffs between noise reduction and delay time with multiple poles. > Just considering the single-sample impulse response of the two > filters, your 4-pole filter has a response much higher (2.5x peak) > and broader than that of the 1-pole "heavy" filter -- even though the > response in the first iteration is indeed identical. That brings up yet another possible metric, the integral of the discrete unit impulse response. This seeks to take into account not only the amplitude but the broadness of the disturbance from a single bad sample. Yes there are many ways of looking at this, each giving you somewhat different guidance. ******************************************************************** Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products (978) 742-9014. Gold level PIC consultants since 2000. --=20 http://www.piclist.com PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .