How about using a Cauer with it's poor phase reponse,but the software compensating for it? Consider the following:- 1. An analogue filter is cascaded with an N-bit ADC feeding an N bit DAC. 2. An analogue filter is cascaded with an N-bit digital filter designed to create a response equal to that above. Will there be a difference between the two responses? Suppose that for the above, we have for: 1. The signal goes straight to the N-bit ADC-DAC. 2. The front end is a resistive divider with a gain of 1/10, and the N-bit digital filter has a gain 10 to give a total response of 1 as above. The quantization noise is 10 times worse in the second case compared to the first, so the answer is yes, there can be one hell of a difference. Funky
Creating brick-wall anti-aliasing filters?
Started by ●March 11, 2004
Reply by ●March 11, 20042004-03-11
Funky wrote:> How about using a Cauer with it's poor phase reponse,but the software > compensating for it? > > > Consider the following:- > > 1. An analogue filter is cascaded with an N-bit ADC feeding an N bit DAC.Pointless as an end result, but perhaps a sensible intermediate design.> 2. An analogue filter is cascaded with an N-bit digital filter designed to > create a response equal to that above.Rethink or restate. There's no way to pass a signal through an analog filter and then a digital filter without a DAC between the filters.> Will there be a difference between the two responses? > > Suppose that for the above, we have for: > 1. The signal goes straight to the N-bit ADC-DAC.Then there is likely to be aliasing.> 2. The front end is a resistive divider with a gain of 1/10, and the N-bit > digital filter has a gain 10 to give a total response of 1 as above.Still no anti-alias filter? Bad news!> The quantization noise is 10 times worse in the second case compared to the > first, so the answer is yes, there can be one hell of a difference.That depends on the signal level. The divider might be needed to avoid overload, with ample signal to keep quantization noise reasonably low.> FunkyEven a straw man needs a firm foundation. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●March 12, 20042004-03-12
"Jerry Avins" <jya@ieee.org> wrote in message news:405128f7$0$2845$61fed72c@news.rcn.com...> Funky wrote: > > > How about using a Cauer with it's poor phase reponse,but the software > > compensating for it? > > > > > > Consider the following:-I should have made myself clear. The example is as simple as possible to show that sofware compensation for an imperfect front end filter can create problems. The example is for a bandlimited signal below the Nyquist sampling frequency and demonstrates the basic problems.> > 1. An analogue filter is cascaded with an N-bit ADC feeding an N bitDAC.> > Pointless as an end result, but perhaps a sensible intermediate design.> > 2. An analogue filter is cascaded with an N-bit digital filter designedto> > create a response equal to that above. > > Rethink or restate. There's no way to pass a signal through an analog > filter and then a digital filter without a DAC between the filters.I thought it trivial to mention the ADC, DAC as part of the digtal filter.> > Will there be a difference between the two responses? > > > > Suppose that for the above, we have for: > > 1. The signal goes straight to the N-bit ADC-DAC. > > Then there is likely to be aliasing.Yes. But lets keep the signal bandlimited to Nyquist, say.> > 2. The front end is a resistive divider with a gain of 1/10, and theN-bit> > digital filter has a gain 10 to give a total response of 1 as above. > > Still no anti-alias filter? Bad news! > > > The quantization noise is 10 times worse in the second case compared tothe> > first, so the answer is yes, there can be one hell of a difference. > > That depends on the signal level. The divider might be needed to avoid > overload, with ample signal to keep quantization noise reasonably low.In case 1, the front end "filter" is optimum for a design with gain 1. In case 2, the software compensates for the attenuation, but it's performance is worse than 1. Hence if designing any anti-aliasing filter with the software compensating for the poor phase response, don't expect it to be as good as a purely hardware anti-aliasing filter. Funky> > Funky > > Even a straw man needs a firm foundation > > Jerry > -- > Engineering is the art of making what you want from things you can get. > ����������������������������������������������������������������������� >
Reply by ●March 13, 20042004-03-13
Funky wrote:> "Jerry Avins" <jya@ieee.org> wrote in message > news:405128f7$0$2845$61fed72c@news.rcn.com... > >>Funky wrote: >> >> >>> How about using a Cauer with it's poor phase reponse,but the software >>>compensating for it? >>> >>> >>>Consider the following:- > > > I should have made myself clear. The example is as simple as possible to > show that sofware compensation for an imperfect front end filter can create > problems.Einstein's Rule: Everything should be as simple as possible, but not simpler.> The example is for a bandlimited signal below the Nyquist sampling frequency > and demonstrates the basic problems.It would have been appropriate to provide that information with the question.>>>1. An analogue filter is cascaded with an N-bit ADC feeding an N bit > > DAC. > >>Pointless as an end result, but perhaps a sensible intermediate design. > > >>>2. An analogue filter is cascaded with an N-bit digital filter designed > > to > >>>create a response equal to that above. >> >>Rethink or restate. There's no way to pass a signal through an analog >>filter and then a digital filter without a DAC between the filters. > > > I thought it trivial to mention the ADC, DAC as part of the digtal filter.Why? If you think that way, you better be careful when reading spec sheets or signing contracts.>>>Will there be a difference between the two responses? >>> >>>Suppose that for the above, we have for: >>>1. The signal goes straight to the N-bit ADC-DAC. >> >>Then there is likely to be aliasing. > > > Yes. But lets keep the signal bandlimited to Nyquist, say. > > >>>2. The front end is a resistive divider with a gain of 1/10, and the > > N-bit > >>>digital filter has a gain 10 to give a total response of 1 as above. >> >>Still no anti-alias filter? Bad news! >> >> >>>The quantization noise is 10 times worse in the second case compared to > > the > >>>first, so the answer is yes, there can be one hell of a difference. >> >>That depends on the signal level. The divider might be needed to avoid >>overload, with ample signal to keep quantization noise reasonably low. > > > In case 1, the front end "filter" is optimum for a design with gain 1.True, but depending on the actual signal level, unity gain may itself not be optimum. You are still making hidden assumptions that affect the answer you want.> In case 2, the software compensates for the attenuation, but it's > performance is worse than 1.If case 1 runs into overload, case 2 is likely to have better performance. Of course, some other gain might be better yet.> Hence if designing any anti-aliasing filter with the software compensating > for the poor phase response, don't expect it to be as good as a purely > hardware anti-aliasing filter.I don't see how that follows in general. It may very well follow under certain conditions, but you haven't stated what they are. Life isn't simple. Engineering is almost as complicated. With design, you need to look at individual cases. It's always tempting to make general rules that cover all instances, but it usually doesn't work. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
