Can A Band Pass Filter Speed Up Lock In Amplification?
in [Basics]
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From: Bob Masta on 4 Jul 2010 12:32 On Sun, 04 Jul 2010 12:59:50 GMT, N0Spam(a)daqarta.com (Bob Masta) wrote: >On Sat, 3 Jul 2010 09:28:23 -0700 (PDT), Bret >Cahill <Bret_E_Cahill(a)yahoo.com> wrote: > >>> >Supposing you cannot get a good clean reference, just another noisy >>> >signal where the second signal is in phase with the first? =A0The >>> >product of two noisy signals is a rectified signal plus ac noise -- >>> >just like in conventional phase sensitive detection except the >>> >magnitude of the rectified signal has no use. =A0If the product of the >>> >two signals isn't desired the only thing the product could be used for >>> >is the frequency which would need to be picked out by tuning another >>> >circuit to that frequency. >>> >>> If the two signals are in phase (implying that >>> they have the same frequency) then when you >>> multiply them together you will get terms at 0 Hz >>> and twice the frequency. Sure, you could tune >>> another circuit to 2f, but then what was the point >>> of the multiplication in the first place? >> >>Wouldn't the multiplication increase the [product signal] SNR? > >It might... I'll have to think about this (and >maybe run some experiments with Daqarta). > >I think the best you could hope for would be a 3 >dB improvement. That's what you'd get if you just >added them together and divided by 2 (synchronous >averaging), assuming that the noise in each signal >is uncorrelated with the other's noise, while the >underlying desired waves are identical. > >But synchronous averaging assumes that the desired >portions of each signal are identical in shape, >frequency, and amplitude. I don't think you >intended to assume identical amplitudes, just >shapes and frequencies. So if the multiplier idea >can deal with different amplitudes, it might be >useful. > >I'll report back tomorrow... Report on multiplication as possible noise reduction strategy: Test signal was a 468.75 Hz sine. (This frequency was set using Daqarta's Line Step option so it is an exact submultiple of the 48000 Hz sample rate and thus produces a perfect single vertical line spectrum, with no "skirts" that would require windowing to reduce.) The sine was at 50% of full-scale (on Daqarta Stream 0), mixed with 50% white noise (on Daqarta Stream 1). This produces a spectrum with the sine spike at -6 dB (relative to full scale) and the noise floor at each frequency at about -36 dB. Across the whole 24 kHz spectrum, the integrated noise (using Daqarta's Sigma cursor option) is -9 dB. So the signal is 3 dB above the noise. (Measurements were made in Daqarta's Spectrum mode using 32-frame Exponential averaging. This better shows the average noise level, at the cost of making the spectrum respond a bit more slowly to transients... which weren't present here.) If two *waveform* frames (1024 samples each) of this signal are synchronously averaged (equivalent to 2 copies of the signal with independent noise sources, since the noise is different for each frame), the tone spike is of course still at -6 dB, but the noise across the band is at -12 dB, a 3 dB improvement, just as predicted by theory. Note: The above measurement was made by setting the waveform averager (Spectrum off) to 2 frames Exponential and starting the average, then toggling to Spectrum. This shows the spectrum of the waveform average, rather than the spectrum average of the waveform. Finally, Daqarta Streams 2 and 3 were created identical to Streams 0 and 1, respectively, except that the Stream 3 noise source was independent from that of Stream 1. To multiply 0+1 times 2+3, Streams 2 and 3 each used AM modulation set to 200% (Daqarta's way of specifying pure multiplication), and each used as its modulation source the sum of Streams 0+1. (When a stream is used as a modulator, it is no longer summed directly to the output.) The overall output was thus: Sine 2 * (Sine 0 + Noise 1) + Noise 3 * (Sine 0 + Noise 1) which is identical to: (Sine 0 + Noise 1) * (Sine 2 + Noise 3) The result was a spectrum with a noise floor at about -40 dB, with spectral lines at 0 and 2f at -18 dB. The noise across the band was -13.5 dB... 4.5 dB *above* the 2f signal spike. So the upshot is that multiplication makes things worse, not better. If you don't have equal-amplitude sines to use for waveform averaging, then one very effective way to distinguish signal from noise is to take an FFT. With a 1024-sample FFT, the signal spike was 30 dB above the noise floor, even though it was only 3 dB above the overall integrated noise. FFTs with more samples reduce the noise floor even further (since the overall noise will be the same, but made up of more small contributions from each frequency). Best regards, Bob Masta DAQARTA v5.10 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!
From: Bret Cahill on 4 Jul 2010 12:27 > >> Is prefiltering or filtering before the phase sensitive detection step > >> of lock in a common practice? > > >> If the signal frequency is in a fairly narrow band, say one octave, > >> can a band pass filter speed up the aquistion time of a lock in? > > >Instead of prefiltering the signal for the signal input, prefilter the > >signal to get something that would trigger a clean reference signal. > > That's what the PLL is there for... it "filters" > the signal you provide to extract the reference. That isn't necessarily the cleanest extraction. > The question is whether there are conditions where > a pre-filter on the PLL would improve overall lock > time, as opposed to changes in the PLL itself. Is there a boot strap or iterative approach? > Dunno about that, but note that since this implies > that you know the desired frequency pretty well, +/- 10% or less. > you might instead choose to apply that knowledge > to the PLL oscillator control. such that in the > absence of a signal it runs at the desired center > frequency, and has an overall frequency range that > matches the known signal range. That might speed > up lock time. > > Just a thought. Thanks again. Bret Cahill > Best regards, > > Bob Masta > > DAQARTA v5.10 > Data AcQuisition And Real-Time Analysis > www.daqarta.com > Scope, Spectrum, Spectrogram, Sound Level Meter > Frequency Counter, FREE Signal Generator > Pitch Track, Pitch-to-MIDI > DaqMusic - FREE MUSIC, Forever! > (Some assembly required) > Science (and fun!) with your sound card!
From: Bret Cahill on 4 Jul 2010 13:27 > >> >Supposing you cannot get a good clean reference, just another noisy > >> >signal where the second signal is in phase with the first? =A0The > >> >product of two noisy signals is a rectified signal plus ac noise -- > >> >just like in conventional phase sensitive detection except the > >> >magnitude of the rectified signal has no use. =A0If the product of the > >> >two signals isn't desired the only thing the product could be used for > >> >is the frequency which would need to be picked out by tuning another > >> >circuit to that frequency. > > >> If the two signals are in phase (implying that > >> they have the same frequency) then when you > >> multiply them together you will get terms at 0 Hz > >> and twice the frequency. Sure, you could tune > >> another circuit to 2f, but then what was the point > >> of the multiplication in the first place? > > >Wouldn't the multiplication increase the [product signal] SNR? > > It might... I'll have to think about this (and > maybe run some experiments with Daqarta). > > I think the best you could hope for would be a 3 > dB improvement. That's what you'd get if you just > added them together and divided by 2 (synchronous > averaging), assuming that the noise in each signal > is uncorrelated with the other's noise, while the > underlying desired waves are identical. The higher the frequency of the noise in each signal the more independent it is of the noise in the other signal. The lower the frequency of the noise the more the same noise appears in both signals. It's probably an inverse relationship between sq rt of frequency and noise correlation, certainly something well known as well behaved. For very low frequency noise the magnitudes as well a phase and frequency are pretty much the same so a clean reference, at least clean of low frequency noise, can be generated simply by subtracting one signal from the other and the PSD multiplication would be: s1(s1 - s2) and s2(s1 - s2) The really high frequency noise, of course, can be filtered with a conventional filter and the really low frequency noise disappears in the subtraction. The problem is near the signal frequency. If the ratio of the magnitude of the noise in one signal that correlates to the other signal's noise was known, then that could appear as a correction factor in the subtractions above. It may require breaking the problem into a lot of bandwidths each with its own ratio. Another solution would be to try to use a frequency higher than most of the noise. This would decrease the SNR so it may not change much. > But synchronous averaging assumes that the desired > portions of each signal are identical in shape, > frequency, and amplitude. I don't think you > intended to assume identical amplitudes, just > shapes and frequencies. The clean signal amplitudes are different. Determining the frequency would be just as good, however, and may be the way to go. > So if the multiplier idea > can deal with different amplitudes, it might be > useful. > > I'll report back tomorrow... Thanks again. Bret Cahill > Best regards, > > Bob Masta > > DAQARTA v5.10 > Data AcQuisition And Real-Time Analysis > www.daqarta.com > Scope, Spectrum, Spectrogram, Sound Level Meter > Frequency Counter, FREE Signal Generator > Pitch Track, Pitch-to-MIDI > DaqMusic - FREE MUSIC, Forever! > (Some assembly required) > Science (and fun!) with your sound card!- Hide quoted text - > > - Show quoted text -
From: Bob Masta on 5 Jul 2010 08:12 On Sun, 4 Jul 2010 10:27:18 -0700 (PDT), Bret Cahill <BretCahill(a)peoplepc.com> wrote: >The higher the frequency of the noise in each signal the more >independent it is of the noise in the other signal. The lower the >frequency of the noise the more the same noise appears in both >signals. > >It's probably an inverse relationship between sq rt of frequency and >noise correlation, certainly something well known as well behaved. This sounds like a very unusual situation, not the behavior of ordinary noise sources. I assume you have some particular case in mind... perhaps if you gave more details the group could give better advice. Best regards, Bob Masta DAQARTA v5.10 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!
From: Bret Cahill on 5 Jul 2010 12:35
> >The higher the frequency of the noise in each signal the more > >independent it is of the noise in the other signal. The lower the > >frequency of the noise the more the same noise appears in both > >signals. > > >It's probably an inverse relationship between sq rt of frequency and > >noise correlation, certainly something well known as well behaved. > > This sounds like a very unusual situation, not the behavior > of ordinary noise sources. I assume you have some > particular case in mind... perhaps if you gave more details > the group could give better advice. The information is in there just like other situations where PSD works. The question is if it can be teased out somehow. Bret Cahill > Best regards, > > Bob Masta > > DAQARTA v5.10 > Data AcQuisition And Real-Time Analysis > www.daqarta.com > Scope, Spectrum, Spectrogram, Sound Level Meter > Frequency Counter, FREE Signal Generator > Pitch Track, Pitch-to-MIDI > DaqMusic - FREE MUSIC, Forever! > (Some assembly required) > Science (and fun!) with your sound card! |