John Monro wrote:> Jerry, > You wrote: > >> John, >> >> Your thoughtful analysis inspired me to think a bit more, but we still >> diverge on many points. I'll address the differences as they arise. >> > I think we diverge mainly on matters of detail and definitions. In the > following I have snipped out everything except your most recent comments. > >> >> I agree that sampling is an on/off process and as such can be said to >> have a DC component. That assumes a mathematical model, but I see a >> physical one.> > > (snip) > >> The sampling waveform I envision controls a switch. Depending on the >> switch design, it may go from 1 to 0, +1 to -1, +12 to +10, or any >> other two-level waveform. > > (snip) > But that is only the controlling waveform which, as you suggest, is > device dependant. I have no problem with the switch concept. It can > be seen as switching between (signal) and (no signal) as with the usual > sampling arrangement, or between(signal) and (inverted signal) in the > arrangement Vencat describes.Do you too consider any form of modulation with a binary waveform to be a form of sampling? I don't. In fact, I see that belief as the misconception that gave rise to this thread.> I recognise what you say about a physical model, but don't think it is > unreasonable to look on the processes as multiplying the signal by > values:(1.000 or 0.000) in the first case and (1.000 or -1.000) in the > other.I do think it's unreasonable. The voltage that is finally quantized is associated with the edge if the control signal that opens the switch. (For a clever and interesting variant, look at the switched-capacitor ADC in the 68HC11 and relatives.)>> He isn't sampling at all. As I wrote above, he's modulating. Elsewhere >> in this thread someone equated chopping and time-division multiplexing >> to sampling. These processes create sidebands ad infinitum, but they >> are not the same process. (Balanced modulation can be seen as TDM of a >> signal and it's inversion.) >> > We agree that he is modulating, but where we seem to differ is that I > claim that conventional sampling is also a modulating process, but using > a very distinctive waveform. I agree that Vencat's square-wave example > can not be regarded as 'sampling' because his modulating signal does not > meet the essential requirement of selecting the signal for a very brief > time, and de-selecting it for the rest of the cycle. > > (snip) > > Jerry, you commented then on some of my numbered points: > >>> >>> 1. The sampling process can be regarded as multiplication in the >>> time-domain of an input signal by the sampling waveform, frequency fs. >> >> >> >> Not any waveform. Multiplying by a symmetric square wave yields AM >> suppressed carrier with harmonics that must be filtered in practice. >> Multiplying by a sine wave yields AM suppressed carrier with no >> harmonics. Multiplying by a train of impulses (all of the same sign) >> yields a train of samples. Confusing the physical implementation of >> sampling with that idealized mathematical representation started this >> thread. >> > I claim though that the representation that I used is a pretty accurate > representation of the physical model you describe, and refers back, in a > non-mathematical way to the known characteristics of modulators. > > There is no confusion! The examples you give are exactly correct, > including the generation of a train of samples. If you look at those > samples though, you see a train of pulses with successive pulses varying > in amplitude in step with the input signal. In other words, the input > signal is modulating the sampling waveform. This produces a series of > double-sideband suppressed carrier signals, each one centred on a > multiple of fs, (including the fundamental, and DC). I claim that this > is a reasonable and accurate way of looking at the process. > > >>> 2, A typical or 'usual' sampling waverform has an amplitude of 1.000 >>> for a few nanoseconds and 0.000 for the rest of the cycle. >> >> >> >> Not in practice. Typically, one closes a switch between the signal and >> a holding capacitor for a substantial interval -- the acquisition time >> -- then opens it to lock in the sample. The opening is not >> instantaneous, so there is an aperture time. The few nanoseconds you >> refer to is the time for the switching element to disconnect. >> > > Correct. For audio sampling the aperture time is microseconds, not > nanoseconds. I have told myself a million times: "Don't exaggerate!" > >> Much of the discussion that follows is an accurate description based >> on the misconception I described above, so I snipped it. Sampling can >> be seen as a special case of amplitude modulation, but not every form >> of modulation (not even every form with a binary carrier) is sampling. >> I see the analysis on non-sampling modulation as irrelevant here. >> > Jerry, you don't seem to make allowance for the fact that I was > responding to Vencat's query. I was trying to give him some > understanding of why his square-wave sampling waveform gave him the > results he observed, and why the usual sampling waveform is the only one > that is useful for sampling. I tied that in to his observation that > when there was no DC in a proposed 'sampling waveform' there was no > baseband in the output. I was not suggesting that people should use any > sampling waveform other than the usual one.The mistake we all made at first was not insisting that, while sampling is a form of amplitude modulation -- a nifty insight -- not every form of amplitude modulation is sampling. Vencat wasn't sampling, and we should have told him so right away.>>> So Jerry (and the group) I hope you will agree that the DC component >>> of the sampling waveform is in fact responsible for the baseband >>> component in the sampled signal. >> >> >> >> I do agree. I hadn't seen it in that light before. > > > It is something that does not seem to be mentioned in the text books. > Since the sampling waveform is by its nature uni-polar, of course it > must have a DC component, but it had not occurred to me until recently > that the DC component alone determines the amplitude of the baseband > signal in the sampled waveform. > > Thanks for an interesting discussion, > > Regards, > John-- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Basic Signal Processing Question
Started by ●July 20, 2005
Reply by ●July 25, 20052005-07-25
Reply by ●July 25, 20052005-07-25
Jerry Avins wrote:> John Monro wrote: > >> Jerry, >> You wrote: >> >>> John, >>> >>> Your thoughtful analysis inspired me to think a bit more, but we >>> still diverge on many points. I'll address the differences as they >>> arise. >>> >> I think we diverge mainly on matters of detail and definitions. In the >> following I have snipped out everything except your most recent comments. >> >>> >>> I agree that sampling is an on/off process and as such can be said to >>> have a DC component. That assumes a mathematical model, but I see a >>> physical one.> >> >> >> (snip) >> >>> The sampling waveform I envision controls a switch. Depending on the >>> switch design, it may go from 1 to 0, +1 to -1, +12 to +10, or any >>> other two-level waveform. >> >> >> (snip) >> But that is only the controlling waveform which, as you suggest, is >> device dependant. I have no problem with the switch concept. It can >> be seen as switching between (signal) and (no signal) as with the >> usual sampling arrangement, or between(signal) and (inverted signal) >> in the arrangement Vencat describes. > > > Do you too consider any form of modulation with a binary waveform to be > a form of sampling? I don't. In fact, I see that belief as the > misconception that gave rise to this thread.No, I never suggested that. If there was any suggestion that modulating with Vencat's square-wave was sampling, it did not come form me. What I did suggest was that modulation with a particular waveform (1.000 briefly, then 0.000)is sampling, and vice-versa.> >> I recognise what you say about a physical model, but don't think it is >> unreasonable to look on the processes as multiplying the signal by >> values:(1.000 or 0.000) in the first case and (1.000 or -1.000) in the >> other. > > > I do think it's unreasonable. The voltage that is finally quantized is > associated with the edge if the control signal that opens the switch. > (For a clever and interesting variant, look at the switched-capacitor > ADC in the 68HC11 and relatives.)It might be associated with that edge, but it is actually the voltage that the capacitor manages to charge to during the time the switch connects the signal voltage-source to the capacitor, taking into account series resistance and inductance, and the fact that the signal voltage is changing during the process. Does it really change my argument though if the multiplying factor is not exactly 1.000, and is very slightly higher or lower due to those practical circuit limitations?> >>> He isn't sampling at all. As I wrote above, he's modulating. >>> Elsewhere in this thread someone equated chopping and time-division >>> multiplexing to sampling. These processes create sidebands ad >>> infinitum, but they are not the same process. (Balanced modulation >>> can be seen as TDM of a signal and it's inversion.) >>> >> We agree that he is modulating, but where we seem to differ is that I >> claim that conventional sampling is also a modulating process, but >> using a very distinctive waveform. I agree that Vencat's square-wave >> example can not be regarded as 'sampling' because his modulating >> signal does not meet the essential requirement of selecting the signal >> for a very brief time, and de-selecting it for the rest of the cycle. >> >> (snip) >> >> Jerry, you commented then on some of my numbered points: >> >>>> >>>> 1. The sampling process can be regarded as multiplication in the >>>> time-domain of an input signal by the sampling waveform, frequency fs. >>> >>> >>> >>> >>> Not any waveform. Multiplying by a symmetric square wave yields AM >>> suppressed carrier with harmonics that must be filtered in practice. >>> Multiplying by a sine wave yields AM suppressed carrier with no >>> harmonics. Multiplying by a train of impulses (all of the same sign) >>> yields a train of samples. Confusing the physical implementation of >>> sampling with that idealized mathematical representation started this >>> thread. >>> >> I claim though that the representation that I used is a pretty >> accurate representation of the physical model you describe, and refers >> back, in a non-mathematical way to the known characteristics of >> modulators. >> >> There is no confusion! The examples you give are exactly correct, >> including the generation of a train of samples. If you look at those >> samples though, you see a train of pulses with successive pulses >> varying in amplitude in step with the input signal. In other words, >> the input signal is modulating the sampling waveform. This produces >> a series of double-sideband suppressed carrier signals, each one >> centred on a multiple of fs, (including the fundamental, and DC). I >> claim that this is a reasonable and accurate way of looking at the >> process. >> >> >>>> 2, A typical or 'usual' sampling waverform has an amplitude of >>>> 1.000 for a few nanoseconds and 0.000 for the rest of the cycle. >>> >>> >>> >>> >>> Not in practice. Typically, one closes a switch between the signal >>> and a holding capacitor for a substantial interval -- the acquisition >>> time -- then opens it to lock in the sample. The opening is not >>> instantaneous, so there is an aperture time. The few nanoseconds you >>> refer to is the time for the switching element to disconnect. >>> >> >> Correct. For audio sampling the aperture time is microseconds, not >> nanoseconds. I have told myself a million times: "Don't exaggerate!" >> >>> Much of the discussion that follows is an accurate description based >>> on the misconception I described above, so I snipped it. Sampling can >>> be seen as a special case of amplitude modulation, but not every form >>> of modulation (not even every form with a binary carrier) is >>> sampling. I see the analysis on non-sampling modulation as irrelevant >>> here. >>> >> Jerry, you don't seem to make allowance for the fact that I was >> responding to Vencat's query. I was trying to give him some >> understanding of why his square-wave sampling waveform gave him the >> results he observed, and why the usual sampling waveform is the only >> one that is useful for sampling. I tied that in to his observation >> that when there was no DC in a proposed 'sampling waveform' there was >> no baseband in the output. I was not suggesting that people should >> use any sampling waveform other than the usual one. > > > The mistake we all made at first was not insisting that, while sampling > is a form of amplitude modulation -- a nifty insight -- not every form > of amplitude modulation is sampling. Vencat wasn't sampling, and we > should have told him so right away. >Yes, a plain statement like that would have been useful.>>>> So Jerry (and the group) I hope you will agree that the DC component >>>> of the sampling waveform is in fact responsible for the baseband >>>> component in the sampled signal. >>> >>> >>> >>> >>> I do agree. I hadn't seen it in that light before. >> >> >> >> It is something that does not seem to be mentioned in the text books. >> Since the sampling waveform is by its nature uni-polar, of course it >> must have a DC component, but it had not occurred to me until recently >> that the DC component alone determines the amplitude of the baseband >> signal in the sampled waveform. >> >> Thanks for an interesting discussion, >> >> Regards, >> John > > >
Reply by ●July 25, 20052005-07-25
> Do you too consider any form of modulation with a binary waveform to be > a form of sampling? I don't. In fact, I see that belief as the > misconception that gave rise to this thread.Yes I do think it is a form of sampling, multiplying (or modulating if you prefer) the signal by any waveform that is sometimes 1 and sometimes 0 is a form of sampling. At the poutput, you don't have the entire signal you have only _samples_ of the signal. Sampling (multiplying or modulating) with a 50% duty factor square wave of 0 and 1 is a special case called natural sampling. Also note, sampling is NOT the same as quantizing. Mark
Reply by ●July 26, 20052005-07-26
Mark wrote:> >>Do you too consider any form of modulation with a binary waveform to be >>a form of sampling? I don't. In fact, I see that belief as the >>misconception that gave rise to this thread. > > > Yes I do think it is a form of sampling, multiplying (or modulating if > you prefer) the signal by any waveform that is sometimes 1 and > sometimes 0 is a form of sampling. At the output, you don't have the > entire signal you have only _samples_ of the signal.Much of the usual treatment of samples applies only to impulsive samples or reasonable approximations of them. I can imagine a tapped analog bucket-brigade delay line and analog multipliers as a transversal filter that works with unquantized impulsive samples. It won't produce similar results when fed the output of a balanced modulator.> Sampling (multiplying or modulating) with a 50% duty factor square > wave of 0 and 1 is a special case called natural sampling.Even there, the high end will roll off more.> Also note, sampling is NOT the same as quantizing.Agreed. However, none of this rather abstruse discussion addresses Venkat's original confusion. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 26, 20052005-07-26
Jerry Avins wrote: (snip)> He isn't sampling at all. As I wrote above, he's modulating. Elsewhere > in this thread someone equated chopping and time-division multiplexing > to sampling. These processes create sidebands ad infinitum, but they are > not the same process. (Balanced modulation can be seen as TDM of a > signal and it's inversion.)Somehow this reminds me of the claims that the device used to connect to a DSL line is not a modem, as it doesn't do any modulation, and that the output is digital not analog. Well, yes, it does modulation, especially since it can't be a baseband signal. There there was the claim that ethernet is digital, and not analog as it is not modulated but manchester encoded. So I claimed that no, it isn't manchester coding but synchronous phase modulation with two possible values for the phase. The distinction between sampling and modulation is complicated, though, especially if filtering is involved. -- glen
Reply by ●July 26, 20052005-07-26
glen herrmannsfeldt wrote:> Jerry Avins wrote: > (snip) > >> He isn't sampling at all. As I wrote above, he's modulating. Elsewhere >> in this thread someone equated chopping and time-division multiplexing >> to sampling. These processes create sidebands ad infinitum, but they >> are not the same process. (Balanced modulation can be seen as TDM of a >> signal and it's inversion.) > > > Somehow this reminds me of the claims that the device used to connect > to a DSL line is not a modem, as it doesn't do any modulation, and > that the output is digital not analog. Well, yes, it does modulation, > especially since it can't be a baseband signal. > > There there was the claim that ethernet is digital, and not analog > as it is not modulated but manchester encoded. So I claimed that no, > it isn't manchester coding but synchronous phase modulation with two > possible values for the phase. > > The distinction between sampling and modulation is complicated, > though, especially if filtering is involved.That's the point. However you want to classify Venkat's process, the usual expectations of the nature of sampled signals don't apply to its products, nor do the text-book ways of dealing with them. Communities sometimes declare roads long before they plan to build them, in order to reserve the paths they take. Sometimes those roads appear on maps. To accept a balanced modulator as a sampler in the Shannon sense is to follow one of those phantom roads into a marsh. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 27, 20052005-07-27
Jerry Avins wrote: (snip, I wrote)>> The distinction between sampling and modulation is complicated, >> though, especially if filtering is involved.> That's the point. However you want to classify Venkat's process, the > usual expectations of the nature of sampled signals don't apply to its > products, nor do the text-book ways of dealing with them.> Communities sometimes declare roads long before they plan to build them, > in order to reserve the paths they take. Sometimes those roads appear on > maps. To accept a balanced modulator as a sampler in the Shannon sense > is to follow one of those phantom roads into a marsh.I don't disagree with that. But do you still consider it sampling if it averages over a finite time instead of a zero width delta function? (As all real samplers do.) As the time approaches the sample rate is it still sampling? Also, even agreeing that a balanced modulator isn't a sampler, before it can be used for FM stereo generation the signals must be band limited. Once they are band limited, all the sampling rules apply. If I have the math right, the output of a stereo multiplexer (without any other subcarriers) can be properly sampled it at 76kHz. (That is just a little surprising since it goes up to 53kHz, though I am not so sure about the 19kHz pilot.) If I had a black box that sampled it at the appropriate frequency and then reconstructed it again, you would not be able to tell that the box had sampled it. I am not so sure about your road analogy, but it seem that there is at least some similarity between the two. -- glen
Reply by ●July 27, 20052005-07-27
glen herrmannsfeldt wrote:> Jerry Avins wrote: > > (snip, I wrote) > >>> The distinction between sampling and modulation is complicated, >>> though, especially if filtering is involved. > > >> That's the point. However you want to classify Venkat's process, the >> usual expectations of the nature of sampled signals don't apply to its >> products, nor do the text-book ways of dealing with them. > > >> Communities sometimes declare roads long before they plan to build >> them, in order to reserve the paths they take. Sometimes those roads >> appear on maps. To accept a balanced modulator as a sampler in the >> Shannon sense is to follow one of those phantom roads into a marsh. > > > I don't disagree with that. > > But do you still consider it sampling if it averages over a finite time > instead of a zero width delta function? (As all real samplers do.) > As the time approaches the sample rate is it still sampling?In common parlance, a sample has a single value. It mat in fact be an average about an instant, or an average leading up to an instant, but it is a single value. A musician's demo CD is a sample of his work; that is not a sample in the signal-processing sense. If a way to express a full-period sample number is specified, then it is real sampling. As the actual sample width becomes greater than about a tenth of the sample period, accurate reconstruction requires frequency compensation.> Also, even agreeing that a balanced modulator isn't a sampler, before > it can be used for FM stereo generation the signals must be band > limited. Once they are band limited, all the sampling rules apply. > > If I have the math right, the output of a stereo multiplexer > (without any other subcarriers) can be properly sampled it at 76kHz. > (That is just a little surprising since it goes up to 53kHz, though I > am not so sure about the 19kHz pilot.)I think the 76 Kc works because baseband isn't needed. Apparently, both L and R can be extracted from the subcarrier and its sidebands.> If I had a black box that sampled it at the appropriate frequency and > then reconstructed it again, you would not be able to tell that the box > had sampled it.But you'd be hard pressed to reconstruct it accurately if the samples were too wide.> I am not so sure about your road analogy, but it seem that there is at > least some similarity between the two.I'm not so sure about it either. Is rang true when I wrote it. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 27, 20052005-07-27
> > In common parlance, a sample has a single value. It may in fact be an > average about an instant, or an average leading up to an instant, but it > is a single value.That is becasue "in common parlance" sampling commonly means sampling ___and quantizing____. But the pure definition of sampling requires only a switch or chopper or if you prefer a modulator or a multiplier and a 1 and 0 sampling signal, nothing more. I agree this discussion has drifted far off topic of the OPs question. thanks Mark
Reply by ●July 27, 20052005-07-27
Mark wrote:> >>In common parlance, a sample has a single value. It may in fact be an >>average about an instant, or an average leading up to an instant, but it >>is a single value. > > > > That is becasue "in common parlance" sampling commonly means sampling > ___and quantizing____.I don't agree. In common parlance, it means sampling and measuring. In CCD image sensors, there are as many samplers as pixels. Sometimes the samples are quantized to produce a digital data stream, sometimes the analog samples are used directly. I suppose one could argue that the charge is quantized because it consists of a theoretically countable number of electrons, but that's a petty quibble in our context. We have gone beyond discussing definitions and into the realm of consensus usage. That's my doing, and I regret it. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
