Anti-aliasing advice for de-interleaved signals
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From: PhilipOrr on 21 Jul 2010 20:12 Hi everyone - this is my first post here. It's about time I joined a DSP forum. I need some advice related to a measurement system. The system samples at 1 kHz but between every sample the input to the DAQ is switched between two inputs. The result is that the acquired signal, at 1 kHz, is two interleaved signals at 500 Hz each. I would then like to go on to separate the two signals, which are a detection of the same measurement but with equal/opposite sensitivities, so that I can find their differential. The idea is that I can use this differential signal to get a measurement that is free from the noise that is common to both channels. I hope I have explained that clearly... Basically I am detecting two interleaved signals which are measurements with opposite sensitivities so that I can subtract them from each other to get a single more sensitive measurement with reduced noise. My query is how and where to implement anti-aliasing filters in this system... I am sampling at 1 kHz then separating the interleaved signals to get two 500 Hz signals. I can then either subtract every consecutive pair (i.e. measurement at 500 Hz which I guess would require me to invert the sign between each subtraction in order to maintain the correct polarity) or, more simply, wait until I have both samples, then produce the subtraction, then wait for another pair, then subtract again (measurement at 250 Hz). I am confusing myself with where to implement anti-aliasing in this sort of scheme before performing FFT on the final signal, and whether the filter should be for 250 or 500 Hz... Thanks for any advice. I need some clarity!
From: Mark on 21 Jul 2010 21:26 On Jul 21, 8:12 pm, "PhilipOrr" <philip.orr(a)n_o_s_p_a_m.eee.strath.ac.uk> wrote: > Hi everyone - this is my first post here. It's about time I joined a DSP > forum. > > I need some advice related to a measurement system. The system samples at 1 > kHz but between every sample the input to the DAQ is switched between two > inputs. The result is that the acquired signal, at 1 kHz, is two > interleaved signals at 500 Hz each. > > I would then like to go on to separate the two signals, which are a > detection of the same measurement but with equal/opposite sensitivities, so > that I can find their differential. The idea is that I can use this > differential signal to get a measurement that is free from the noise that > is common to both channels. > > I hope I have explained that clearly... Basically I am detecting two > interleaved signals which are measurements with opposite sensitivities so > that I can subtract them from each other to get a single more sensitive > measurement with reduced noise. > > My query is how and where to implement anti-aliasing filters in this > system... > > I am sampling at 1 kHz then separating the interleaved signals to get two > 500 Hz signals. I can then either subtract every consecutive pair (i.e. > measurement at 500 Hz which I guess would require me to invert the sign > between each subtraction in order to maintain the correct polarity) or, > more simply, wait until I have both samples, then produce the subtraction, > then wait for another pair, then subtract again (measurement at 250 Hz). > > I am confusing myself with where to implement anti-aliasing in this sort of > scheme before performing FFT on the final signal, and whether the filter > should be for 250 or 500 Hz... > > Thanks for any advice. I need some clarity! I think you need to use two separate AA filters, one for each channel. and you are sampling each channel at 500 sps so the two filters need to be 250Hz or less. Mark
From: Tim Wescott on 21 Jul 2010 22:00 On 07/21/2010 05:12 PM, PhilipOrr wrote: > Hi everyone - this is my first post here. It's about time I joined a DSP > forum. > > I need some advice related to a measurement system. The system samples at 1 > kHz but between every sample the input to the DAQ is switched between two > inputs. The result is that the acquired signal, at 1 kHz, is two > interleaved signals at 500 Hz each. > > I would then like to go on to separate the two signals, which are a > detection of the same measurement but with equal/opposite sensitivities, so > that I can find their differential. The idea is that I can use this > differential signal to get a measurement that is free from the noise that > is common to both channels. > > I hope I have explained that clearly... Basically I am detecting two > interleaved signals which are measurements with opposite sensitivities so > that I can subtract them from each other to get a single more sensitive > measurement with reduced noise. > > My query is how and where to implement anti-aliasing filters in this > system... > > I am sampling at 1 kHz then separating the interleaved signals to get two > 500 Hz signals. I can then either subtract every consecutive pair (i.e. > measurement at 500 Hz which I guess would require me to invert the sign > between each subtraction in order to maintain the correct polarity) or, > more simply, wait until I have both samples, then produce the subtraction, > then wait for another pair, then subtract again (measurement at 250 Hz). > > I am confusing myself with where to implement anti-aliasing in this sort of > scheme before performing FFT on the final signal, and whether the filter > should be for 250 or 500 Hz... > > Thanks for any advice. I need some clarity! So the signal out of the DAC is something like x_dac[n] = x[n] + offset if n is even, and x_dac[n] = offset - x[n] if n is odd? Are you proposing to do the anti-aliasing before sampling or after? There's not much point (or meaning) to anti-aliasing after sampling, unless you're going to decimate. If you think about it, you're sampling the actual signal at 1kHz. So anti-alias filtering appropriate to that sample rate _ahead_ of the modulating process would work. Alternately, if you know that there isn't much energy in the signal (or noise) at or above Nyquist, you may not want to do anti-alias filtering at all. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
From: Jerry Avins on 21 Jul 2010 23:27 On 7/21/2010 8:12 PM, PhilipOrr wrote: > Hi everyone - this is my first post here. It's about time I joined a DSP > forum. > > I need some advice related to a measurement system. The system samples at 1 > kHz but between every sample the input to the DAQ is switched between two > inputs. The result is that the acquired signal, at 1 kHz, is two > interleaved signals at 500 Hz each. > > I would then like to go on to separate the two signals, which are a > detection of the same measurement but with equal/opposite sensitivities, so > that I can find their differential. The idea is that I can use this > differential signal to get a measurement that is free from the noise that > is common to both channels. > > I hope I have explained that clearly... Basically I am detecting two > interleaved signals which are measurements with opposite sensitivities so > that I can subtract them from each other to get a single more sensitive > measurement with reduced noise. > > My query is how and where to implement anti-aliasing filters in this > system... > > I am sampling at 1 kHz then separating the interleaved signals to get two > 500 Hz signals. I can then either subtract every consecutive pair (i.e. > measurement at 500 Hz which I guess would require me to invert the sign > between each subtraction in order to maintain the correct polarity) or, > more simply, wait until I have both samples, then produce the subtraction, > then wait for another pair, then subtract again (measurement at 250 Hz). > > I am confusing myself with where to implement anti-aliasing in this sort of > scheme before performing FFT on the final signal, and whether the filter > should be for 250 or 500 Hz... > > Thanks for any advice. I need some clarity! You ought to take a single measurement of a differential signal. Look into using an instrumentation amplifier in front of the anti-alias filter that precedes ADC. (You wrote DAC, but I don't think you meant that.) Subtracting one signal from another displaced 2 ms won't provide much noise cancellation, even at 60 Hz. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: Vladimir Vassilevsky on 22 Jul 2010 00:43
Jerry Avins wrote: > On 7/21/2010 8:12 PM, PhilipOrr wrote: > >> Hi everyone - this is my first post here. It's about time I joined a DSP >> forum. >> >> I need some advice related to a measurement system. The system samples >> at 1 >> kHz but between every sample the input to the DAQ is switched between two >> inputs. The result is that the acquired signal, at 1 kHz, is two >> interleaved signals at 500 Hz each. >> >> I would then like to go on to separate the two signals, which are a >> detection of the same measurement but with equal/opposite >> sensitivities, so >> that I can find their differential. > You ought to take a single measurement of a differential signal. Look > into using an instrumentation amplifier in front of the anti-alias > filter that precedes ADC. BTW, I measured the CMRR of LT1167, and I was amazed to see ~130dB. It would be hard to achieve that kind of performance in digital, especially considering the ADC impairments. > that.) Subtracting one signal from another displaced 2 ms won't provide > much noise cancellation, even at 60 Hz. You can make for the time shift by interpolation. Clay Turner-ish approach with the same interpolator filter used for delaying and advancing the signal by 2 ms in the corresponding channels. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com |