Integration w/o Smoothing; Demodulate, Integrate and then Take the Quotient
in [DSP]
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From: Bret Cahill on 20 Feb 2010 00:54 > Greed is the root of Eating like a pig is the root of all obesity. Bret Cahill
From: George Herold on 20 Feb 2010 23:48 On Feb 20, 12:52 am, Bret Cahill <BretCah...(a)peoplepc.com> wrote: > > > There is no reason to smooth after demodulation in some low noise lock > > > in amplifier situations. > > More generally, if you are only trying to reduce the noise by a > limited amount. > > > > > > > > If you are taking the quotient of two signals that are identical > > > except for magnitude and noise, i.e., shape, frequency and phase > > > angle, simply low pass integrate each signal after each is multiplied > > > by the reference. > > > > Once the S/N ratio is high enough simply take the quotient without > > > wasting time to smooth either signal. > > > > No smoothing of either demodulated signal is necessary because the > > > rectified humps appear in both the numerator and denominator in phase > > > and with the same relative size as the quotient. > > > > This is important in low noise situations where there isn't time to > > > smooth the humps. > > > > This simple filtering solution should be fairly common in electronics.. > > > > Bret Cahill > > > What is smoothing? > > Say a rectifier outputs a voltage proportional to |sinwt|. It's not a > constant DC voltage. > > If you want a constant DC voltage then you must smooth somehow. > > > "simply low pass integrate each signal after each is multiplied > > > by the reference." > > Low pass filtering is smoothing. > > Which takes time even if the noise in an ac signal is low or non > existent. > > If you are taking a quotient of two low noise signals as in the OP, > however, then no smoothing of each (ref.) X (signal) output is > necessary. You only need to integrate just long enough to reduce the > noise to an acceptable level. > > Any voltage fluctuations due to the signals will cancel in the > quotient. > > Bret Cahill- Hide quoted text - > > - Show quoted text - Do you have any 'scope pictures to share of your quotient idea. If you've got a known frequency, low noise signal, then you can sample synchronosly(sp.) and get a measure of the signal size with no low pass filtering. George H.
From: Bret Cahill on 21 Feb 2010 12:22 > > > > There is no reason to smooth after demodulation in some low noise lock > > > > in amplifier situations. > > > More generally, if you are only trying to reduce the noise by a > > limited amount. > > > > > If you are taking the quotient of two signals that are identical > > > > except for magnitude and noise, i.e., shape, frequency and phase > > > > angle, simply low pass integrate each signal after each is multiplied > > > > by the reference. > > > > > Once the S/N ratio is high enough simply take the quotient without > > > > wasting time to smooth either signal. > > > > > Nosmoothingof either demodulated signal is necessary because the > > > > rectified humps appear in both the numerator and denominator in phase > > > > and with the same relative size as the quotient. > > > > > This is important in low noise situations where there isn't time to > > > > smooth the humps. > > > > > This simple filtering solution should be fairly common in electronics. > > > > >BretCahill > > > > What issmoothing? > > > Say a rectifier outputs a voltage proportional to |sinwt|. It's not a > > constant DC voltage. > > > If you want a constant DC voltage then you must smooth somehow. > > > > "simply low pass integrate each signal after each is multiplied > > > > by the reference." > > > Low pass filtering issmoothing. > > > Which takes time even if the noise in an ac signal is low or non > > existent. > > > If you are taking a quotient of two low noise signals as in the OP, > > however, then nosmoothingof each (ref.) X (signal) output is > > necessary. You only need to integrate just long enough to reduce the > > noise to an acceptable level. > > > Any voltage fluctuations due to the signals will cancel in the > > quotient. > > >BretCahill- Hide quoted text - > > > - Show quoted text - > > Do you have any 'scope pictures to share of your quotient idea. With a divider circuit you could model it on SPICE. Make up your own noise with a lot of voltage sources. It would be easier to make up each signal, the sum of sinwt (the clean signal) and cos(vt+phi) (the noise) terms and then multiply by a ref. sinwt and then integrate to the same time for both signals. And then divide to see if it homes in on a const. number > If you've got a known frequency, low noise signal, then you can sample > synchronosly(sp.) and get a measure of the signal size with no low > pass filtering. The goal is to get the noise down from 5 - 20% to below 0.5% so any tactic that might be commonly used to do that is of interest here. It may very well end up digital as that can be cost effective as well as more flexible but it would be very surprising if this situation isn't very common and a similar analog solution didn't appear decades ago, long before netbooks cost $200. Bret Cahill
From: George Herold on 21 Feb 2010 18:27 On Feb 21, 12:22 pm, Bret Cahill <BretCah...(a)peoplepc.com> wrote: > > > > > There is no reason to smooth after demodulation in some low noise lock > > > > > in amplifier situations. > > > > More generally, if you are only trying to reduce the noise by a > > > limited amount. > > > > > > If you are taking the quotient of two signals that are identical > > > > > except for magnitude and noise, i.e., shape, frequency and phase > > > > > angle, simply low pass integrate each signal after each is multiplied > > > > > by the reference. > > > > > > Once the S/N ratio is high enough simply take the quotient without > > > > > wasting time to smooth either signal. > > > > > > Nosmoothingof either demodulated signal is necessary because the > > > > > rectified humps appear in both the numerator and denominator in phase > > > > > and with the same relative size as the quotient. > > > > > > This is important in low noise situations where there isn't time to > > > > > smooth the humps. > > > > > > This simple filtering solution should be fairly common in electronics. > > > > > >BretCahill > > > > > What issmoothing? > > > > Say a rectifier outputs a voltage proportional to |sinwt|. It's not a > > > constant DC voltage. > > > > If you want a constant DC voltage then you must smooth somehow. > > > > > "simply low pass integrate each signal after each is multiplied > > > > > by the reference." > > > > Low pass filtering issmoothing. > > > > Which takes time even if the noise in an ac signal is low or non > > > existent. > > > > If you are taking a quotient of two low noise signals as in the OP, > > > however, then nosmoothingof each (ref.) X (signal) output is > > > necessary. You only need to integrate just long enough to reduce the > > > noise to an acceptable level. > > > > Any voltage fluctuations due to the signals will cancel in the > > > quotient. > > > >BretCahill- Hide quoted text - > > > > - Show quoted text - > > > Do you have any 'scope pictures to share of your quotient idea. > > With a divider circuit you could model it on SPICE. Make up your own > noise with a lot of voltage sources. > > It would be easier to make up each signal, the sum of sinwt (the clean > signal) and cos(vt+phi) (the noise) terms and then multiply by a ref. > sinwt and then integrate to the same time for both signals. > > And then divide to see if it homes in on a const. number > > > If you've got a known frequency, low noise signal, then you can sample > > synchronosly(sp.) and get a measure of the signal size with no low > > pass filtering. > > The goal is to get the noise down from 5 - 20% to below 0.5% so any > tactic that might be commonly used to do that is of interest here. > > It may very well end up digital as that can be cost effective as well > as more flexible but it would be very surprising if this situation > isn't very common and a similar analog solution didn't appear decades > ago, long before netbooks cost $200. > > Bret Cahill- Hide quoted text - > > - Show quoted text - Got any pictures of what you call noise and what is signal. (Or I guess to put it another way, is your noise fundamental. (Thermal noise, shot noise and amplifer noise.) or is it something else? George H.
From: Raymond Yohros on 5 Mar 2010 17:09
On Feb 19, 11:10 pm, John Larkin <jjlar...(a)highNOTlandTHIStechnologyPART.com> wrote: > On Fri, 19 Feb 2010 07:59:17 -0800 (PST), Bret Cahill > > > > <BretCah...(a)peoplepc.com> wrote: > >There is no reason to smooth after demodulation in some low noise lock > >in amplifier situations. > > >If you are taking the quotient of two signals that are identical > >except for magnitude and noise, i.e., shape, frequency and phase > >angle, simply low pass integrate each signal after each is multiplied > >by the reference. > > >Once the S/N ratio is high enough simply take the quotient without > >wasting time to smooth either signal. > > >No smoothing of either demodulated signal is necessary because the > >rectified humps appear in both the numerator and denominator in phase > >and with the same relative size as the quotient. > > >This is important in low noise situations where there isn't time to > >smooth the humps. > > >This simple filtering solution should be fairly common in electronics. > > But it's not. So the possibilities are... > > 1. It's been thought of before, but it doesn't work > > or > > 2. You, law clerk or whatever you are, thought of it first, and tens > of thousands of control engineers, over the last 100 years, missed it. > > John > > who never was a big fan of dividing by zero. > dividing by zero gives errors in the message window but its useful when you just want to cut off the signal. |