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Electronics Forum / Basics / July 2009Noise Is 3 Orders of Magnitude Greater Than A Wave Form
Everything is known about the transmitted wave, i.e., the shape & phase angle, except the amplitude. All that is necessary is to recover is the amplitude of the wave. Can this be done when the noise is several orders of magnitude greater than the signal? Bret Cahill > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. [quoted text clipped - 4 lines] > > Bret Cahill Narrowing the final detection bandwidth is the only hope. If the noise spectrum is white, narrow bandwidth through averaging works. If you cannot average, there is trouble. The old lockin amplifiers used a modulation or chopping signal and a long time constant in the final filter. I had signals at times that required an hour of integration to detect. It was slow but it worked. > > Everything is known about the transmitted wave, i.e., the shape & > > phase angle, except the amplitude. [quoted text clipped - 12 lines] > at times that required an hour of integration to detect. It > was slow but it worked. I forgot to mention that the signal wave form can be anything that can be generated. For example, if something similar to an AM radio signal, say, f(t) = (sint)(sin10t)(sin10t) was possible and the frequency of the noise was about the same as the sin(t) factor, then f(t) will plot the noise every time f(t) = 0. In this case that would be ten times as often as the sin(t) factor. The noise can then be subtracted to recover the wave form. Bret Cahill >> > Everything is known about the transmitted wave, i.e., the shape & >> > phase angle, except the amplitude. [quoted text clipped - 26 lines] > >Bret Cahill I think what's happening is that you have 1. Defined the noise to be bandlimited to radian frequencies below about 1 and 2. Up-converted (modulated) the signal to have usable (recoverable) components around 10 times that frequency. So (am I allowed to say 'duh'?) a simple highpass filtering operation will remove the noise from the upconverted signal. You moved the signal to where you knew there was no noise. It's more interesting when the signal and the noise occupy the same bandwidth. John > >> > Everything is known about the transmitted wave, i.e., the shape & > >> > phase angle, except the amplitude. [quoted text clipped - 31 lines] > 1. Defined the noise to be bandlimited to radian frequencies below > about 1 The noise and the signal are both low and have about the same frequency, ~ x/2pi. There is little that can be done to change this situation. There is no time to wait more than several cycles for the result either. > and > > 2. Up-converted (modulated) the signal to have usable (recoverable) > components around 10 times that frequency. To plot the noise. Every time sin 10t = 0, f(t) = zero, and the only thing left is the low frequency noise. Then a high pass filter can smooth out the (sin10t)(sin10t) component so something like the original signal can still be recovered after the noise is subtracted out. Alternatively traditional filters can be eliminated altogether. The signal + noise as well as the noise alone can be traced out from the high frequency signal. The noise is then subtracted from the signal + noise to recover the signal. > So (am I allowed to say 'duh'?) a simple highpass filtering operation > will remove the noise from the upconverted signal. You moved the > signal to where you knew there was no noise. Plot f(t) and it's easy to see the original signal sill exists, although in a somewhat discontinuous form. It would be interesting if this has never been done before. Bret Cahill >> >> > Everything is known about the transmitted wave, i.e., the shape & >> >> > phase angle, except the amplitude. [quoted text clipped - 44 lines] >To plot the noise. Every time sin 10t = 0, f(t) = zero, and the only >thing left is the low frequency noise. You are assuming the ability to high-frequency modulate the signal before the noise is added to it. So you already know what the noiseless signal looks like. John > >> >> > Everything is known about the transmitted wave, i.e., the shape & > >> >> > phase angle, except the amplitude. [quoted text clipped - 48 lines] > before the noise is added to it. So you already know what the > noiseless signal looks like. As I said in the OP, "Everything is known about the transmitted wave, i.e., the shape & phase angle, except the amplitude." This works for the same reason reading a newspaper in a foreign language is easy. You already know what they are going to say. Bret Cahill >> >> >> > Everything is known about the transmitted wave, i.e., the shape & >> >> >> > phase angle, except the amplitude. [quoted text clipped - 56 lines] > >Bret Cahill Are you familiar with the way a lockin amplifier works? That sounds maybe like what you are doing. If you know everything about the signal but its amplitude, then you have or can construct a normalized (unity amplitude) version of it. That will positively correlate with the unknown-amplitude version of the signal but have zero correlation to random noise. Things like IR absorption spectrometers commonly chop (square wave modulate) the light source and recover the signal with a synchronous rectifier. That washes out any noise picked up in the optical path or the detector. Things like this commonly dig signals out from 1000x the noise... but slowly. If the noise is known to be bandlimited, it's a lot easier... almost cheating. John > >> >> >> > Everything is known about the transmitted wave, i.e., the shape & > >> >> >> > phase angle, except the amplitude. [quoted text clipped - 58 lines] > > Are you familiar with the way a lockin amplifier works? Many thanks for the tip but phase lag is just a more sophisticated form of filtering which is valuable in many situations where the noise is all over the spectrum. This is not filtering noise; it's measuring it then subtracting it. Basically the signal is brought to zero to identify the noise. Then the noise is subtracted from whatever the receiver is putting out. For an accurate signal measurement both the noise and the noise + signal output from the receiver must be known to a higher accuracy. Integrating should yield that higher accuracy but it isn't always necessary as it can work over _one single higher frequency wave cycle_. > That sounds > maybe like what you are doing. If you know everything about the signal [quoted text clipped - 11 lines] > If the noise is known to be bandlimited, it's a lot easier... almost > cheating. I ran it by a lawyer and he said it was completely legal. Bret Cahill >> >> >> >> > Everything is known about the transmitted wave, i.e., the shape & >> >> >> >> > phase angle, except the amplitude. [quoted text clipped - 62 lines] >form of filtering which is valuable in many situations where the noise >is all over the spectrum. A lockin doesn't work by phase lag; it works by correlation. >This is not filtering noise; it's measuring it then subtracting it. > >Basically the signal is brought to zero to identify the noise. Then >the noise is subtracted from whatever the receiver is putting out. That only works if the zero+measure thing is done at or above the noise's Nyquist frequency, and that is in turn only meaningful if the noise is bandlimited. And you are able somehow to turn the signal on and off at that rate. So all you need is a highpass filter. But the math algorithm you describe is about equivalent. >For an accurate signal measurement both the noise and the noise + >signal output from the receiver must be known to a higher accuracy. [quoted text clipped - 20 lines] > >I ran it by a lawyer and he said it was completely legal. I thought you *were* a lawyer. John > That only works if the zero+measure thing is done at or above the > noise's Nyquist frequency, and that is in turn only meaningful if the > noise is bandlimited. The noise frequency is limited to about +/- 50% - 75% of the signal frequency. > And you are able somehow to turn the signal on and off at that rate. > So all you need is a highpass filter. You'ld lose the signal with a simple filter. > But the math algorithm you > describe is about equivalent. The signal is transformed to something that has a lot of the characteristics of the original signal. For example, the integral is 1/2 the integral of the original curve. The advantage is the transformed curve plots out the difference between the noise and the transformed signal. Then the noise is subtracted. That is not a conventional filter. Bret Cahill > The advantage is the transformed curve plots out the difference > between the noise and the transformed signal. Then the noise is > subtracted. > > That is not a conventional filter. It's an unconventional way of implementing a filter, but it's still a filter, and the end result will be equivalent to using some conventional filter to separate the carrier from the noise. I'm not saying your technique won't work. Quite likely it could be made to work. But it won't work any *better* than using conventional AM modulation and filtering. It can't, for fundamental mathematical reasons.  SignatureGreg > > The advantage is the transformed curve plots out the difference > > between the noise and the transformed signal. Then the noise is [quoted text clipped - 4 lines] > It's an unconventional way of implementing a filter, > but it's still a filter, It would be interesting if it's unconventional. I came up with it a few minutes after the OP killing time because of a delay. > and the end result will be > equivalent to using some conventional filter to [quoted text clipped - 4 lines] > any *better* than using conventional AM modulation > and filtering. The system will not respond in the same way as to a conventional AM wave form. For one thing, higher frequencies are attenuated more than lower frequencies. The higher frequency here only changes sign as often as the signal wave so the media doesn't "see" a +/- high frequency AM wave but something much like the original low frequency signal. > It can't, for fundamental mathematical > reasons. Bret Cahill > The higher frequency here only changes sign as often as the signal > wave so the media doesn't "see" a +/- high frequency AM wave but > something much like the original low frequency signal. As long as the medium is linear, this makes no difference. There's nothing special about the zero crossings. SignatureGreg > > The higher frequency here only changes sign as often as the signal > > wave so the media doesn't "see" a +/- high frequency AM wave but > > something much like the original low frequency signal. > > As long as the medium is linear, this makes no difference. > There's nothing special about the zero crossings. Can you have the same resonance as the original signal? Bret Cahill > > The advantage is the transformed curve plots out the difference > > between the noise and the transformed signal. Then the noise is [quoted text clipped - 15 lines] > -- > Greg Fundamentally, I have a major problem with the discussion. and its not the fact that people are fishing their lines of pursuit, which miss the fundamental. The info was NEVER posted. And Jon, your earlier post-given freely had a portion copy of my work pre-last semester which I did give freely. And I already gave you a consideration. The sensor receives the loud noise, say, 10sin(0.7x), plus the small signal, say, sin(x ). The signal, however, can be transformed into sin (x)sin^2(100x) so the sensor receives (10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 This can be viewed by pasting the entire line into www.wolframalpha.com The blue area is the signal to be extracted from the noise. It's over the noise to the left of x = pi and under the noise to the right of pi. The high frequency curve runs between the signal and the noise and maps out both curves to any precision depending on frequency and regression. Bret Cahill > > > Everything is known about the transmitted wave, i.e., the shape & > > > phase angle, except the amplitude. [quoted text clipped - 28 lines] > > - Show quoted text - > The sensor receives the loud noise, say, 10sin(0.7x), plus the small > signal, say, sin(x ). The signal, however, can be transformed into sin > (x)sin^2(100x) so the sensor receives > > (10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4 What you are doing is changing the problem. You are now looking at a sin(100x) modulated by sin(x). This says the noise and the signal are independent of one another. If you can do this, make it 1000x and make you life easier. > This can be viewed by pasting the entire line into www.wolframalpha.com > [quoted text clipped - 40 lines] >> >>- Show quoted text - > > The sensor receives the loud noise, say, 10sin(0.7x), plus the small > > signal, say, sin(x ). The signal, however, can be transformed into sin [quoted text clipped - 3 lines] > > What you are doing is changing the problem. As I pointed out above, I forgot to mention in the OP that the designer could change the signal to suit the problem. > You are now looking at a > sin(100x) modulated by sin(x). Actually it's a sin^2(100x) which is always positive. Sin100x will not work as the sign of the original signal must be preserved. For example, try pasting (10sin(0.7x) + sin(x)sin(100x)) x from 2 to 3.4 into www.wolframalpha.com How would you know the noise curve? > This says the noise and the signal > are independent of one another. Bingo! > If you can do this, make it 1000x > and make you life easier. In some situations it may be difficult to use very high frequencies. That's why regression was mentioned. Bret Cahill >>>The sensor receives the loud noise, say, 10sin(0.7x), plus the small >>>signal, say, sin(x ). The signal, however, can be transformed into sin [quoted text clipped - 14 lines] > Sin100x will not work as the sign of the original signal must be > preserved. Sin(100x) will work just fine. To detect sin(x) just multiply the signal by sin(100x) again or, to be careful multiply by sin(100x) and also by cos(100x). This does a quadrature detection and the magnitude of the two term is independent of the phase relative to sin(100x) > For example, try pasting > [quoted text clipped - 3 lines] > > How would you know the noise curve? The point of using the high frequency is to remove your signal from the noise value. >>This says the noise and the signal >>are independent of one another. [quoted text clipped - 7 lines] > > That's why regression was mentioned. The physics requirements are always the same. You need to have the signal power greater than the noise power in the detection bandwidth. Any fancy processing scheme is just trying to narrow the detection bandwidth. > Bret Cahill > >>>The sensor receives the loud noise, say, 10sin(0.7x), plus the small > >>>signal, say, sin(x ). The signal, however, can be transformed into sin [quoted text clipped - 16 lines] > > Sin(100x) will work just fine. The shape and the effect of the original signal, sin x, on the rest of the system cannot be preserved if the sign of the high frequency factor alternates each cycle. > To detect sin(x) just multiply > the signal by sin(100x) again or, to be careful multiply by [quoted text clipped - 9 lines] > > > How would you know the noise curve? > The point of using the high frequency is to remove your > signal from the noise value. And this is done by first identifying the noise curve. The high frequency curve and, therefore, the entire f(t), will equal 0 on every cycle of the high frequency. Since we know when the signal is zero we know the value of the noise at that time. > >>This says the noise and the signal > >>are independent of one another. [quoted text clipped - 3 lines] > >>If you can do this, make it 1000x > >>and make you life easier. > > In some situations it may be difficult to use very high frequencies. > > That's why regression was mentioned. > The physics requirements are always the same. You need to have the > signal power greater than the noise power in the detection bandwidth. Not if you can identify the noise to 99.995% accuracy. > Any fancy processing scheme is just trying to narrow the detection > bandwidth. I didn't think the approach above was either fancy or "narrowing the bandwith." Obviously, if the noise frequency is about the same as signal frequency it will necessary to end run the use of conventional filters altogether. It would be interesting to learn if and when something similar was tried. Bret Cahill >> > The sensor receives the loud noise, say, 10sin(0.7x), plus the small >> > signal, say, sin(x ). The signal, however, can be transformed into sin [quoted text clipped - 11 lines] > >Actually it's a sin^2(100x) which is always positive. Which is equivalent to 100% amplitude modulating at 200x. Square wave chopping would work, too. That's more common in synchronous detection instruments. John >>>>The sensor receives the loud noise, say, 10sin(0.7x), plus the small >>>>signal, say, sin(x ). The signal, however, can be transformed into sin [quoted text clipped - 18 lines] > > John Bret apparently has decided he knows physics and signal processing better than all of us. I have no idea why he is posting since he claims we are all wrong. He seems to think the laws of physics do not apply to him. What are the ‘Five Pillars’ of Islam? August 31st, 2008 I would be thankful if you give my article 5 minute of your value time. THANK YOU What are the ‘Five Pillars’ of Islam? They are the framework of the Muslim life: faith, prayer, concern for the needy, self-purification, and the pilgrimage to Makkah for those who are able. First Pillar: Faith There is no god worthy of worship except God and Muhammad is His messenger. This declaration of faith is called the Shahada, a simple formula which all the faithful pronounce. In Arabic, the first part is la ilaha illa’Llah - ‘there is no god except God’; ilaha (god) can refer to anything which we may be tempted to put in place of God– wealth, power, and the like. Then comes illa’Llah: ‘except God’, the source of all Creation. The second part of the Shahada is Muhammadun rasulu’Llah: ‘Muhammad is the messenger of God.’ A message of guidance has come through a man like ourselves. Second Pillar: Prayer Salat is the name for the obligatory prayers which are performed five times a day, and are a direct link between the worshiper and God. There is no hierarchical authority in Islam, and no priests, so the prayers are led by a learned person who knows the Quran, chosen by the congregation. These five prayers contain verses from the Quran, and are said in Arabic, the language of the Revelation, but personal supplication can be offered in one’s own language. Prayers are said at dawn, noon, mid-afternoon, sunset and nightfall, and thus determine the rhythm of the entire day. Although it is preferable to worship together in a mosque, a Muslim may pray almost anywhere, such as in fields, offices, factories and universities. Visitors to the Muslim world are struck by the centrality of prayers in daily life. A translation of the Call to Prayer is: ‘God is most great. God is most great. God is most great. God is most great. I testify that there is no god except God. I testify that there is no god except God. I testify that Muhammad is the messenger of God. I testify that Muhammad is the messenger of God. Come to prayer! Come to prayer! Come to success (in this life and the Hereafter)! Come to success! God is most great. God is most great. There is no god except God.’ Once Muslims prayed towards Jerusalem, but during the Prophet’s lifetime it was changed to Makkah. From the minbar, the pulpit, the Imam who leads the prayer gives the sermon at the Friday noon community prayers. Third Pillar: Zakat One of the most important principles of Islam is that all things belong to God, and that wealth is therefore held by human beings in trust. The word zakat means both ‘purification’ and ‘growth’. Our possessions are purified by setting aside a proportion for those in need, and, like the pruning of plants, this cutting back balances and encourages new growth. Each Muslim calculates his or her own zakat individually. For most purposes this involves the payment each year of two and a half percent of one’s capital. A pious person may also give as much as he or she pleases as sadaqa, and does so preferably in secret. Although this word can be translated as ‘voluntary charity’ it has a wider meaning. The Prophet (SAW) said: ‘Even meeting your brother with a cheerful face is charity.’ The Prophet (SAW) said: ‘Charity is a necessity for every Muslim.’ He was asked: ‘What if a person has nothing?’ The Prophet (SAW) replied: ‘He should work with his own hands for his benefit and then give something out of such earnings in charity.’ The Companions asked: ‘What if he is not able to work?’ The Prophet (SAW) said: ‘He should help poor and needy persons.’ The Companions further asked ‘What if he cannot do even that?’ The Prophet (SAW) said ‘He should urge others to do good.’ The Companions said ‘What if he lacks that also?’ The Prophet (SAW) said ‘He should check himself from doing evil. That is also charity.’ Fourth Pillar: The Fast Every year in the month of Ramadan, all Muslims fast from first light until sundown, abstaining from food, drink, and sexual relations. Those who are sick, elderly, or on a journey, and women who are pregnant or nursing are permitted to break the fast and make up an equal number of days later in the year. If they are physically unable to do this, they must feed a needy person for every day missed. Children begin to fast (and to observe the prayer) from puberty, although many start earlier. Although the fast is most beneficial to the health, it is regarded principally as a method of self purification. By cutting oneself off from worldly comforts, even for a short time, a fasting person gains true sympathy with those who go hungry as well as growth in one’s spiritual life. Fifth Pillar: The Pilgrimage (Hajj) The annual pilgrimage to Makkah, the Hajj, is an obligation only for those who are physically and financially able to perform it. Nevertheless, about two million people go to Makkah each year from every comer of the globe providing a unique opportunity for those of different nations to meet one another. Although Makkah is always filled with visitors, the annual Hajj begins in the twelfth month of the Islamic year (which is lunar, not solar, so that Hajj and Ramadan fall sometimes in summer, sometimes in winter). Pilgrims wear special clothes: simple garments which strip away distinctions of class and culture, so that all stand equal before God. The rites of the Hajj, which are of Abrahamic origin, include circling the Ka’ba seven times, and going seven times between the mountains of Safa and Marwa as did Hagar during her search for water. Then the pilgrims stand together on the wide plain of Arafa and join in prayers for God’s forgiveness, in what is often thought of as a preview of the Last Judgment. In previous centuries the Hajj was an arduous undertaking. Today, however, Saudi Arabia provides millions of people with water, modem transport, and the most up-to-date health facilities. The close of the Hajj is marked by a festival, the Eid al-Adha, which is celebrated with prayers and the exchange of gifts in Muslim communities everywhere. This, and the Eid al-Fitr, a feast-day commemorating the end of Ramadan, are the main festivals of the Muslim calendar. —————————————- For more information about Islam http://english.islamway.com/ http://www.islamhouse.com/ http://www.discoverislam.com/ http://www.islambasics.com/index.php http://english.islamway.com/ http://www.islamtoday.net/english/ http://www.islamweb.net/ver2/MainPage/indexe.php http://www.sultan.org/ Contact Us At Imanway.group@gmail.com >What are the Five Pillars of Islam? >August 31st, 2008 >I would be thankful if you give my article 5 minute of your value >time. --- OK, I read your article and now I have a question for you: If Allah is all-powerful and knows the future, then he knows what is going to happen from moment to moment, and how we live our lives is unimportant since he will know in advance what we will do with them. On the other hand, if we can exercise free will, then Allah can't predict the future and isn't, as you claim, omniscient. I've posed this question, many times, to you people, but have not yet received a response of any kind. I don't suppose this time will be any different. JF >Bret apparently has decided he knows physics and signal >processing better than all of us. I have no idea why he >is posting since he claims we are all wrong. He seems >to think the laws of physics do not apply to him. --- Cahill is nothing more than a troll who posts for attention. JF >>>>>The sensor receives the loud noise, say, 10sin(0.7x), plus the small >>>>>signal, say, sin(x ). The signal, however, can be transformed into sin [quoted text clipped - 23 lines] >is posting since he claims we are all wrong. He seems >to think the laws of physics do not apply to him. He seems to have some idea for a gedget that needs synchronous detection to do some measurement. But of course he'll never reveal what he's actually trying to do. And he won't do any research on how everybody else has been doing it for 60 years or so. John > > > Everything is known about the transmitted wave, i.e., the shape & > > > phase angle, except the amplitude. [quoted text clipped - 24 lines] > > The noise can then be subtracted to recover the wave form. I saw something that _might_ be similar/analogous in an old patent. The inventor was using the resonant frequency of the modulating wave to increase S/N. This is not directly possible with conventional AM. I was considering the same approach so it may be the same thing. Bret Cahill > Everything is known about the transmitted wave, i.e., the shape & > phase angle, except the amplitude. [quoted text clipped - 4 lines] > > Bret Cahill ask comp.dsp >Everything is known about the transmitted wave, i.e., the shape & >phase angle, except the amplitude. > >All that is necessary is to recover is the amplitude of the wave. Can >this be done when the noise is several orders of magnitude greater >than the signal? In principle, this can be done with synchronous averaging. I have a tutorial series starting here: <http://www.daqarta.com/tm01.htm> The basic idea is that you must be able to sample the signal synchronously with the sourve (transmitted) wave. That means you need some sort of trigger signal derived directly from the source. On each trigger, you acquire some number of samples, a long enough series for your needs. Here you will want the series long enough to encompass at least one waveform cycle, since you are looking for amplitude of the overall wave. Let's say that you acquire 1024 samples per trigger. (It's generally OK to miss triggers, as long as you always start acquisition on a trigger.) Then you add those 1024 samples, one by one, into a 1024-bin accumulator. The accumulator will end up holding the average value of the waveform, assuming that the waveform is constant and the noise is not synchronous. For every doubling of the number of samples you add into the accumulator, the S/N improves by 3 dB. The overall improvement is thus determined by how long you want to wait to accumulate enough samples. This is the technique used to monitor "evoked potentials" in the brain. For example, the subject is presented with a series of repeating tone bursts of a given frequency, while scalp electrodes monitor brain activity. The source of the tone bursts is also the trigger for the averager. The brain response to any given burst is hopelessly buried in noise, since the scalp electrodes see all the brain activity, not just the auditory part. Only a tiny part of the total is due to the auditory response, but that part is in synchrony with the stimulus, while the rest of the brain in general is not. So after several thousand tone bursts, you can "see" the auditory response. This is used to test hearing in lab animals and infants who can't report what they hear. Best regards, Bob Masta DAQARTA v4.51 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter FREE Signal Generator Science with your sound card! > >Everything is known about the transmitted wave, i.e., the shape & > >phase angle, except the amplitude. > >All that is necessary is to recover is the amplitude of the wave. Can > >this be done when the noise is several orders of magnitude greater > >than the signal? > In principle, this can be done with synchronous > averaging. I have a tutorial series starting > here: > <http://www.daqarta.com/tm01.htm> > The basic idea is that you must be able to sample > the signal synchronously with the sourve > (transmitted) wave. That means you need some sort > of trigger signal derived directly from the > source. That was the plan. Complete control over and knowledge of the source wave should provide some options to recover the signal, even if the noise is orders of magnitude more than than the source wave. Kind of like the military shooting down a tank of hydrazine with a transponder on it and then claiming they took out a satellite. > On each trigger, you acquire some number > of samples, a long enough series for your needs. > Here you will want the series long enough to > encompass at least one waveform cycle, since you > are looking for amplitude of the overall wave. The system will attenuate the low frequency wave more than a high frequency wave that isn't part of the low frequency wave. Determining the amount of attenuation of the low frequency wave was, in fact, the goal. The high frequency component, however, should attenuate much like the low frequency wave if it is tracing out the low frequency wave. > Let's say that you acquire 1024 samples per > trigger. (It's generally OK to miss triggers, as [quoted text clipped - 4 lines] > waveform, assuming that the waveform is constant > and the noise is not synchronous. > For every doubling of the number of samples you > add into the accumulator, the S/N improves by 3 > dB. The overall improvement is thus determined by > how long you want to wait to accumulate enough > samples. Maybe 5 - 7 cycles at most. At first I thought a more sophisticated version of resonant frequency, i.e., lots of different frequency waves added together, might have been a solution but there wasn't enough time to get past the transient effects. > This is the technique used to monitor "evoked > potentials" in the brain. For example, the [quoted text clipped - 24 lines] > FREE Signal Generator > Science with your sound card! >The system will attenuate the low frequency wave more than a high >frequency wave that isn't part of the low frequency wave. [quoted text clipped - 4 lines] >The high frequency component, however, should attenuate much like the >low frequency wave if it is tracing out the low frequency wave. If the medium has different attenuation at different frequencies, emphatically no. The measured attenuation will be the attenuation at the modulating carrier frequency (complicated by sidebands) and not the attenuation of the baseline signal. Your proposed modulation (multiplying by a sin^2 waveform) is even more complex than regular AM, because it includes a baseband component too. Radio stations filter that bit out. (Actually, to get the full solution, you'd have to compute the entire spectrum of the complex modulated signal, and run each spectral line through the transfer function of the process, then recombine. Could get messy.) If the attenuation is flat over frequency, why bother to modulate? Just measure at a high frequency, above the range of the bandlimited noise. You can't fool Mother Nature with simple tricks. John > >The system will attenuate the low frequency wave more than a high > >frequency wave that isn't part of the low frequency wave. [quoted text clipped - 9 lines] > the modulating carrier frequency (complicated by sidebands) and not > the attenuation of the baseline signal. How would that change the overall strategy? Even the original low frequency signal without noise is attenuated somewhat by the medium. The real problem is getting a really precise 4 - 5 sig fig reading from the receiver to be able to have something meaningful left over after the noise is subtracted out. . . . > If the attenuation is flat over frequency, why bother to modulate? In this case it isn't flat. High frequency waves are attenuated more than low frequency. . . . > You can't fool Mother Nature with simple tricks. At least two famous physicists including Hawkings say that it's impossible to destroy even the smallest part of a signal no matter how hard you try. I could be walking down the street minding my own business and get _ambushed_ by this 2 nano volt signal. Bret Cahill >> >The system will attenuate the low frequency wave more than a high >> >frequency wave that isn't part of the low frequency wave. [quoted text clipped - 12 lines] >How would that change the overall strategy? Even the original low >frequency signal without noise is attenuated somewhat by the medium. But the modulated signal doesn't have the same spectral components of the original (baseband) signal. If the attenuation is different at higher frequencies, the modulated signal isn't a surrogate for the low frequency attenuation. If the attenuation measurement at high frequencies is still useful, just use a high frequency signal, bandpass filter, and dump the modulation concept. >The real problem is getting a really precise 4 - 5 sig fig reading >from the receiver to be able to have something meaningful left over [quoted text clipped - 6 lines] >In this case it isn't flat. High frequency waves are attenuated more >than low frequency. Then the modulated signal is not representative of the low frequency attenuation. >. . . > [quoted text clipped - 6 lines] >I could be walking down the street minding my own business and get >_ambushed_ by this 2 nano volt signal. I'm working on a wideband preamp (audio to 20 MHz) looking for a roughly 1 nv signal. About the best wideband amps you can build have a nv of noise per root Hertz of measurement bandwidth, if, IF you do everything right. You're bumping up against fundamental sampling and information theory limits. It's like conservation of energy: all sorts of tricks look feasible, but every one is blocked by nature, in simple or sometimes very sneaky ways. John > >> >The system will attenuate the low frequency wave more than a high > >> >frequency wave that isn't part of the low frequency wave. [quoted text clipped - 17 lines] > higher frequencies, the modulated signal isn't a surrogate for the low > frequency attenuation. It doesn't need to be identical in every respect. > If the attenuation measurement at high > frequencies is still useful, just use a high frequency signal, > bandpass filter, and dump the modulation concept. That would depend on how much it is attenuated. > >The real problem is getting a really precise 4 - 5 sig fig reading > >from the receiver to be able to have something meaningful left over [quoted text clipped - 3 lines] > > >> If the attenuation is flat over frequency, why bother to modulate? > >In this case it isn't flat. High frequency waves are attenuated more > >than low frequency. > Then the modulated signal is not representative of the low frequency > attenuation. Even if it wasn't it could still yield a useful number. > >> You can't fool Mother Nature with simple tricks. > >At least two famous physicists including Hawkings say that it's > >impossible to destroy even the smallest part of a signal no matter how > >hard you try. > >I could be walking down the street minding my own business and get > >_ambushed_ by this 2 nano volt signal. [quoted text clipped - 8 lines] > feasible, but every one is blocked by nature, in simple or sometimes > very sneaky ways. There no mystery to this. A simple error analysis will show a 0.00001% error here will result in a 500% error there. If they ever quantified the measurements/determinations made at the Wimbledon men's finals, i.e. the d theta/dt of the racket, the sig figs might be higher than the $ figs. Bret Cahill > > You can't fool Mother Nature with simple tricks. > > At least two famous physicists including Hawkings say that it's > impossible to destroy even the smallest part of a signal no matter how > hard you try. Yeah, but... this is the leadin to a discussion of Laplace's demon. The signal isn't destroyed, but its information content can easily be made VERY hard to find. Since the uncertainty principle became established, we've been really clear that information in a signal can become meaningless added to thermal noise. A whisper doesn't carry far, we all know. The reason, is that without the low frequency part of our voices (the formants), the rest of vocalization is such broadband high frequencies that thermal noise in the atmosphere masks it. Yesterday's whisper is no longer audible. > <http://www.daqarta.com/tm01.htm> I'm not saying your approach won't work in my case but your Fig. 1 isn't exactly my situation. My noise + signal, if you could see which was which, would look like a large smooth curve with a much smaller amplitude sin curve with a similar period superimposed just above it and/or just below it. My solution was to multiply a high frequency _always positive_ wave onto the original signal. The new signal is discontinuous but it still looks and acts a lot like the original. The difference is every time the high frequency wave was zero, the entire function would be zero and only the noise would remain. The noise is smooth so it could be accurately determined by numerical regression even if the high frequency signal wasn't all that high. Once the noise is known it can be subtracted from the entire output from the receiver. The noise needs to be known to at least 4 decimal place accuracy. Bret Cahill >><http://www.daqarta.com/tm01.htm> > > I'm not saying your approach won't work in my case but your Fig. 1 > isn't exactly my situation. It is the same situation just the spectrum of the noise is different. In all of this, the game is the same because the physics is the same. To get a signal to noise ratio or signal to interference ratio larger than one, you need a bandwidth where the noise is smaller than the signal. Averaging, which is applying a narrow bandpass filter helps most for random noise. > My noise + signal, if you could see which was which, would look like a > large smooth curve with a much smaller amplitude sin curve with a > similar period superimposed just above it and/or just below it. Just how similar a period? The closer the two are, the harder your job is. > My solution was to multiply a high frequency _always positive_ wave > onto the original signal. Life might be simpler if you just multiplied your signal by a square wave whose value is 0 or 1. > The new signal is discontinuous but it still looks and acts a lot like > the original. [quoted text clipped - 6 lines] > Once the noise is known it can be subtracted from the entire output > from the receiver. What you are describing is not noise but interference. > The noise needs to be known to at least 4 decimal place accuracy. That is a tall order. > Bret Cahill > >><http://www.daqarta.com/tm01.htm> > > I'm not saying your approach won't work in my case but your Fig. 1 > > isn't exactly my situation. > It is the same situation just the spectrum of the noise is different. Which is everything when you want to reduce noise. > In all of this, the game is the same because the physics is the > same. The math is entirely different. A smooth low frequency noise curve can be sampled fewer times over longer intervals and the result can be very accurate, especially with regression. > To get a signal to noise ratio or signal to interference ratio > larger than one, you need a bandwidth where the noise is smaller > than the signal. Convert the signal to a higher frequency wave form that still has characteristics of the original signal. > Averaging, which is applying a narrow bandpass > filter helps most for random noise. Time = money. If the average takes more than a few cycles, the result won't be any good for other reasons. > > My noise + signal, if you could see which was which, would look like a > > large smooth curve with a much smaller amplitude sin curve with a > > similar period superimposed just above it and/or just below it. > Just how similar a period? Maybe 0.5 - 1.5. Say the sensor is getting something like 100sin(1.3t) [the noise] + sint [the signal]. I need to know the signal to 0.25% accuracy. > The closer the two are, the harder your > job is. Total control the signal should be worth _something_. > > My solution was to multiply a high frequency _always positive_ wave > > onto the original signal. > Life might be simpler if you just multiplied your signal by a > square wave whose value is 0 or 1. What's the advantage? > > The new signal is discontinuous but it still looks and acts a lot like > > the original. > > The difference is every time the high frequency wave was zero, the > > entire function would be zero and only the noise would remain. The > > noise is smooth so it could be accurately determined by numerical > > regression even if the high frequency signal wasn't all that high. > > Once the noise is known it can be subtracted from the entire output > > from the receiver. > What you are describing is not noise but interference. > > The noise needs to be known to at least 4 decimal place accuracy. > That is a tall order. If it's not possible there's a completely different approach. Bret Cahill >>>><http://www.daqarta.com/tm01.htm> > [quoted text clipped - 4 lines] > > Which is everything when you want to reduce noise. No, the same considerations apply. You need a bandwidth where the ratio of signal to noise meets your requirement. >>In all of this, the game is the same because the physics is the >>same. > > The math is entirely different. A smooth low frequency noise curve > can be sampled fewer times over longer intervals and the result can be > very accurate, especially with regression. No, what you are claiming above is for noise that has a vastly different spectral content than the signal. >>To get a signal to noise ratio or signal to interference ratio >>larger than one, you need a bandwidth where the noise is smaller >>than the signal. > > Convert the signal to a higher frequency wave form that still has > characteristics of the original signal. That has no effect on the SNR since the noise gets converted too. >>Averaging, which is applying a narrow bandpass >>filter helps most for random noise. > > Time = money. If the average takes more than a few cycles, the result > won't be any good for other reasons. If the signal is really one thousandth of the noise, and the noise is random, you need to average a million traces to get an SNR of one. This is because the SNR increases as the square root of the number of traces averaged. >>>My noise + signal, if you could see which was which, would look like a >>>large smooth curve with a much smaller amplitude sin curve with a [quoted text clipped - 8 lines] > > I need to know the signal to 0.25% accuracy. So you want a bandpass filter at frequency t which has skirts down 120db at 1.3t (assuming the noise signal is narrow band and that it is 1000 times the signal amplitude originally). >>The closer the two are, the harder your >>job is. > > Total control the signal should be worth _something_. Knowing the frequency and phase is already factored in the discussion. >>>My solution was to multiply a high frequency _always positive_ wave >>>onto the original signal. [quoted text clipped - 3 lines] > > What's the advantage? You get to look at the signal 50% of the time and the noise 50% of the time to get their relative amplitudes. >>>The new signal is discontinuous but it still looks and acts a lot like >>>the original. [quoted text clipped - 14 lines] > > If it's not possible there's a completely different approach. I would go after that. > Bret Cahill > Convert the signal to a higher frequency wave form that still has > characteristics of the original signal. Yes, certainly. *If* you have a suitable noise-free frequency band available, this is quite easy to do. No revolutionary techniques are required. Your example assumes that you do indeed have such a band available, at about 100x the original signal frequency, and wide enough to accommodate the bandwidth of your signal. In that case, the problem is easy to solve. Just modulate your signal onto a carrier somehow (you're using AM, but you could just as well use FM or some other technique), use a filter at the receiving end to separate the carrier from the noise, and then demodulate. Although it might not seem that way, this *is* what you are effectively doing. You're just using a somewhat unconventional technique to do the filtering and demodulation. There may be simpler ways, e.g. instead of sampling the zero crossings to cancel the noise, just sample the peaks and troughs of the carrier to measure its amplitude. You don't strictly need to know the exact frequency and phase of the carrier, although if you do happen to know it, you can take advantage of that to simplify any sample-oriented processing you want to do. What others are talking about concerning averaging is what you need to do if you *don't* have a noise-free band available, and you've no choice but to deal with signal and noise together in the same band. In that case, the only way to reduce noise is to reduce the receiver's bandwith *somehow*, and averaging is one way to achieve that -- and knowing the frequency and phase of your carrier is a big help, because it lets you implement a synchronous detector. But as I said, you're assuming that you *can* find a noise-free band, so you don't need averaging (except maybe over a few cycles of your carrier frequency, which is much higher than your signal frequency). SignatureGreg > > Convert the signal to a higher frequency wave form that still has > > characteristics of the original signal. > Yes, certainly. *If* you have a suitable noise-free > frequency band available, this is quite easy to do. > No revolutionary techniques are required. The situation is so common and the applications so widespread and the solution such a short distance "off trail" I was assuming they already had 10,000 dirt cheap off-the-shelf versions of it as they generally do in electronics. That was the reason for the OP. Someone was supposed to answer, "TI sells exactly what you want in their 87WA3 series. Anyone can wire 'em up in 5 minutes. I used them for blah blah blah . . ." I was expecting / hoping for more responses like the www.DAQARTA.com guy's. It was only later that I came up with the sin^2 method and that was presented mostly to clarify the OP, not to answer it. > Your example assumes that you do indeed have such > a band available, at about 100x the original signal > frequency, and wide enough to accommodate the > bandwidth of your signal. Or the squared modulated signal. > In that case, the problem is easy to solve. Just > modulate your signal onto a carrier somehow (you're > using AM, but you could just as well use FM or some > other technique), For lack of better terms I used/abused the AM/FM analogy on the two basic solutions that led me here in the first place. The one I was calling "FM" circumvents the noise issue altogether and has an easy to enter niche market but the "AM" one has a noise issue but is much cheaper and has a much larger market. So I had the FM/AM mindset too but true/conventional AM doesn't square the high frequency wave. This is a critical difference. > use a filter at the receiving end > to separate the carrier from the noise, and then > demodulate. > Although it might not seem that way, this *is* what > you are effectively doing. You're just using a > somewhat unconventional technique to do the filtering > and demodulation. So I have until July 2, 2010 to file a PPA. > There may be simpler ways, e.g. > instead of sampling the zero crossings to cancel the > noise, just sample the peaks and troughs of the > carrier to measure its amplitude. Actually that would _not_ work. My background isn't signal processing but now I'm starting to wonder if the hold up behind the larger solution might be traceable to a hold up in electronics. > You don't strictly need to know the exact frequency > and phase of the carrier, although if you do happen > to know it, you can take advantage of that to > simplify any sample-oriented processing you want to > do. > What others are talking about concerning averaging > is what you need to do if you *don't* have a noise-free [quoted text clipped - 5 lines] > of your carrier is a big help, because it lets you > implement a synchronous detector. > But as I said, you're assuming that you *can* find a > noise-free band, so you don't need averaging (except > maybe over a few cycles of your carrier frequency, > which is much higher than your signal frequency). Some California physicist suggested it was impossible to destroy information and recently S. Hawkings agreed. Shred and burn your notes then put the ashes on a rocket headed toward a black hole and 10^68 years from now they'll know what you were trying to hide. The same holds for DNA and your life experiences so everyone is in effect immortal. That's one very good reason to believe efforts at reducing noise / getting information will be fruitful. I don't want to wait 10^67 years for it but then again, I'm not trying to destroy it either. Bret Cahill >> >><http://www.daqarta.com/tm01.htm> > [quoted text clipped - 4 lines] > >Which is everything when you want to reduce noise. Not everything. >> In all of this, the game is the same because the physics is the >> same. [quoted text clipped - 9 lines] >Convert the signal to a higher frequency wave form that still has >characteristics of the original signal. Great as long as you don't do that to the noise, too. John > >Convert the signal to a higher frequency wave form that still has > >characteristics of the original signal. > > Great as long as you don't do that to the noise, too. I'm still expecting some scholar to say this was done in the early 1880s. Bret Cahill In sci.physics Bret Cahill <BretCahill@aol.com> wrote: >> >Convert the signal to a higher frequency wave form that still has >> >characteristics of the original signal. [quoted text clipped - 5 lines] > > Bret Cahill Actually in 1918 by Edwin Armstrong. SignatureJim Pennino Remove .spam.sux to reply. On Jul 4, 10:45 am, j...@specsol.spam.sux.com wrote: > In sci.physics Bret Cahill <BretCah...@aol.com> wrote: > [quoted text clipped - 9 lines] > > Actually in 1918 by Edwin Armstrong. Amplitude of the high(er) frequency wave is modulated by the signal curve. Put sinxsin^2(10x) into www.wolframalpha.com to see the difference with the common AM radio signal. Bret Cahill In sci.physics Bret Cahill <BretCahill@aol.com> wrote: > On Jul 4, 10:45 am, j...@specsol.spam.sux.com wrote: >> In sci.physics Bret Cahill <BretCah...@aol.com> wrote: [quoted text clipped - 20 lines] > > Bret Cahill Who cares and it is irrelevant to what I posted. SignatureJim Pennino Remove .spam.sux to reply. > >> >> >Convert the signal to a higher frequency wave form that still has > >> >> >characteristics of the original signal. [quoted text clipped - 19 lines] > > Who cares The people who click on threads on signal recovery. > and it is irrelevant to what I posted. Feel free to start your own thread on whatever you are interested in. Bret Cahill In sci.physics Bret Cahill <BretCahill@aol.com> wrote: >> >> >> >Convert the signal to a higher frequency wave form that still has >> >> >> >characteristics of the original signal. [quoted text clipped - 27 lines] > > Bret Cahill Feel free to take your meds. SignatureJim Pennino Remove .spam.sux to reply. On Jul 5, 9:00 am, j...@specsol.spam.sux.com wrote: > In sci.physics Bret Cahill <BretCah...@aol.com> wrote: > [quoted text clipped - 21 lines] > > >> Who cares > > The people who click on threads on signal recovery. > >> and it is irrelevant to what I posted. > > Feel free to start your own thread on whatever you are interested in. > Feel free to take your meds. Just admit to yourself what is obvious to everyone else. You never had any interest in this subject in the first place. The dunces are like a bunch of chickens or school of mackerel. They are attracted to anything shiny. Then they reveal that they are dunces. Bret Cahill "When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him." -- Jonathan Swift In sci.physics Bret Cahill <BretCahill@peoplepc.com> wrote: > On Jul 5, 9:00 am, j...@specsol.spam.sux.com wrote: >> In sci.physics Bret Cahill <BretCah...@aol.com> wrote: [quoted text clipped - 40 lines] > > Bret Cahill Yet more babble. SignatureJim Pennino Remove .spam.sux to reply. "When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him." -- Jonathan Swift In sci.physics Bret Cahill <BretCahill@peoplepc.com> wrote: > "When a true genius appears in the world, you may know him by this > sign, that the dunces are all in confederacy against him." > > -- Jonathan Swift But the fact that some geniuses were laughed at does not imply that all who are laughed at are geniuses. They laughed at Columbus, they laughed at Fulton, they laughed at the Wright Brothers. But they also laughed at Bozo the Clown. Carl Sagan SignatureJim Pennino Remove .spam.sux to reply. "When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him." -- Jonathan Swift In sci.physics Bret Cahill <BretCahill@peoplepc.com> wrote: > "When a true genius appears in the world, you may know him by this > sign, that the dunces are all in confederacy against him." > > -- Jonathan Swift But the fact that some geniuses were laughed at does not imply that all who are laughed at are geniuses. They laughed at Columbus, they laughed at Fulton, they laughed at the Wright Brothers. But they also laughed at Bozo the Clown. Carl Sagan SignatureJim Pennino Remove .spam.sux to reply. On Jul 6, 8:00 am, j...@specsol.spam.sux.com wrote: > In sci.physics Bret Cahill <BretCah...@peoplepc.com> wrote: > [quoted text clipped - 9 lines] > > Carl Sagan "So what if I'm a clown?" -- Nietzsche On Jul 5, 10:00 pm, j...@specsol.spam.sux.com wrote: > But the fact that some geniuses were laughed at does not imply that all > who are laughed at are geniuses. They laughed at Columbus, they laughed > at Fulton, they laughed at the Wright Brothers. But they also laughed at > Bozo the Clown. > > Carl Sagan Carl Sagan was the Bozo the Clown of science... On Jul 5, 10:00 pm, j...@specsol.spam.sux.com wrote: > But the fact that some geniuses were laughed at does not imply that all > who are laughed at are geniuses. They laughed at Columbus, they laughed > at Fulton, they laughed at the Wright Brothers. But they also laughed at > Bozo the Clown. > > Carl Sagan Carl Sagan was the Bozo the Clown of science... ==================================== Took over from Einstein, did he? > > But the fact that some geniuses were laughed at does not imply that all > > who are laughed at are geniuses. They laughed at Columbus, they laughed [quoted text clipped - 6 lines] > ==================================== > Took over from Einstein, did he? Sagan was a Nobel laureate? Bret Cahill >> > But the fact that some geniuses were laughed at does not imply that all >> > who are laughed at are geniuses. They laughed at Columbus, they laughed [quoted text clipped - 9 lines] > > Sagan was a Nobel laureate? Even Bozo the Clown could be sensible when he wasn't performing in front of an audience. http://tinyurl.com/c53cqo http://www.androcles01.pwp.blueyonder.co.uk/QUESTION.htm > > But the fact that some geniuses were laughed at does not imply that all > > who are laughed at are geniuses. They laughed at Columbus, they laughed [quoted text clipped - 4 lines] > > Carl Sagan was the Bozo the Clown of science... Sagan, supposedly a popularizer of astronomy, was not really all that competent at public relations or politics either. I once mentioned the nuclear winter theory -- it may be perfectly valid science -- that the well intentioned Sagan thought would disuade the monied interest classes from supporting Reagan's defense buildup. The democratizing effects of global nuclear war would be a political monkey wrench. Would that tactic work? My father went nuclear on that one: BRET, THAT'S THE MOST STUPID IDEA I'VE EVER HEARD OF IN MY ENTIRE LIFE! THAT WILL N E V E R WORK. THEY'LL BE GRABBING AFTER THE MONEY RIGHT ON UP UNTIL THE SECOND THE BOMBS GO OFF . . . I fled the house at that point. Bret Cahill > > "When a true genius appears in the world, you may know him by this > > sign, that the dunces are all in confederacy against him." [quoted text clipped - 7 lines] > > Carl Sagan A good clown is much more likely to be a genius that the average person. Bret Cahill >>><http://www.daqarta.com/tm01.htm> >> [quoted text clipped - 7 lines] >than the signal. Averaging, which is applying a narrow bandpass >filter helps most for random noise. Note that synchronous waveform averaging is *not* a filter, and does not affect the bandwidth of the recovered signal in the least. You still get sharp transients, for example, if they were present in the original. Synchronous waveform averaging will reject any signal that is not synchronous with the trigger, not just random noise. Best regards, Bob Masta DAQARTA v4.51 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter FREE Signal Generator Science with your sound card! > >> I'm not saying your approach won't work in my case but your Fig. 1 > >> isn't exactly my situation. [quoted text clipped - 5 lines] > >than the signal. Averaging, which is applying a narrow bandpass > >filter helps most for random noise. > Note that synchronous waveform averaging is *not* > a filter, and does not affect the bandwidth of the > recovered signal in the least. That's also true for the squared higher frequency sin wave method of subtracting noise. A conventional filter doesn't determine the amplitude of the noise and then subtract it. A conventional filter just attenuates noise above or below a certain bandwith. If the noise is about the same frequency as the signal, then a conventional filter will not work. > You still get > sharp transients, for example, if they were > present in the original. Filters can toss information as well as noise. > Synchronous waveform averaging will reject any > signal that is not synchronous with the trigger, > not just random noise. The higher frequency sin^2 method doesn't require an average. In one application all it takes is one period of ["sampling" by] the high frequency wave to determine the noise as well as the signal. Using regression and integrating over even part of the period of a smooth low frequency noise wave would yield very high precision, even if the "sampling" rate was fairly low. > DAQARTA v4.51 > Data AcQuisition And Real-Time Analysis > www.daqarta.com Can you reduce smooth well behaved low frequency noise by 99.995%? Bret Cahill > A conventional filter doesn't determine the > amplitude of the noise and then subtract it. A conventional filter > just attenuates noise above or below a certain bandwith. But your method doesn't completely eliminate the noise either. You're approximating it by interpolation, and assuming that the result is "good enough". There will always be some residual error -- and that error is just the same as the residual amount of noise that a conventional filter with equivalent passband characteristics would let through. > Filters can toss information as well as noise. So can your method, since you're assuming you can interpolate between signal samples as well. To the extent that's not exactly right, you've lost information. SignatureGreg >> >> I'm not saying your approach won't work in my case but your Fig. 1 >> >> isn't exactly my situation. [quoted text clipped - 14 lines] >amplitude of the noise and then subtract it. A conventional filter >just attenuates noise above or below a certain bandwith. Just a word of caution about the general scheme of subtracting noise: I suspect that variations on this have been re-invented repeatedly, since it sounds like such a great idea. The problem is that when you actually go to implement it you find the big "gotcha": It totally depends upon perfect phase and amplitude matching. If you subtract a version of the noise with a slight time or phase or level shift, the performance goes downhill drastically, and can even be worse than the raw signal. In other words, it will be very hard to make this work as a robust system. Best regards, Bob Masta DAQARTA v4.51 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter FREE Signal Generator Science with your sound card! > >> >> I'm not saying your approach won't work in my case but your Fig. 1 > >> >> isn't exactly my situation. [quoted text clipped - 19 lines] > this have been re-invented repeatedly, since it > sounds like such a great idea. It's surprising that a quick way of explaining why it won't work hasn't appeared as is generally the case in electronics. Certainly some scholarly type somewhere has a comprehensive list of signal processing theories and equipment. > The problem is > that when you actually go to implement it you find > the big "gotcha": It totally depends upon perfect > phase and amplitude matching. That's not an issue if a smooth noise has a period several times longer than the higher frequency wave. The higher frequency wave and the signal that modulates it would clearly appear w/o any synchronization. Put 5sin(1.2x) + sinxsin^2(5x) into www.wolframalpha.com The original signal sinx can be easily retrieved without knowing the phase or even the exact frequency of the modulated wave. > If you subtract a > version of the noise with a slight time or phase > or level shift, the performance goes downhill > drastically, and can even be worse than the raw > signal. In other words, it will be very hard to > make this work as a robust system. The obvious problem with the subtracting approach is the sensor must be much more precise to get a good measurement from the difference of two large numbers. If you wanted to be +/- 1% accurate and the noise was 100 times larger than the signal, then the sensor would need 4 sig fig accuracy. The period of the noise is so long, however, the sensor could rezero itself just before and just after each signal measurement. > DAQARTA v4.51 > Data AcQuisition And Real-Time Analysis > www.daqarta.com > Scope, Spectrum, Spectrogram, Sound Level Meter > FREE Signal Generator > Science with your sound card! Can you eliminate 99.9975% of noise? Bret Cahill |
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