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#161
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Wind/Solar Electrics ???
Your sampling of only the bandwidth information is not
complete for decoding. "Ray Andraka" wrote in message news:zIdsf.34359$Mi5.7331@dukeread07... SolarFlare wrote: The point is the sampling rate has to be done at just over double the frequency of the signal and not the bandwidth. No, that is not correct. It only needs to be sampled at 2x the bandwidth, assuming the spectrum has been properly filtered to energy outside the signal of interest. See my earlier post. |
#162
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Wind/Solar Electrics ???
Now you have to provide samples ***AND*** changing
information with an algorthm to decode successfully. Your samples are then not complete and useless without other information supplied. Superhetrodyning in a radio assumes a variable superhetrodyning frequency when it gets decoded Let's see you regenerate the original carrier and information from that without the carrier frequency known. When you listen to the audio on your radio can you tell the carrier frequency without the dial? "Joel Kolstad" wrote in message ... Assuming all the "information" (the carrier and whatever sideband(s) you care about) is still within your bandpass frequencies, you've lost nothing and there is no aliasing with any non-zero signals. Superheterodyning is still common to get the RF down to an IF that can be digitized directly. As Ray mentioned earlier, the problem with trying to digitize, say, a narrowband 900MHz signal using a 5Msps ADC is that the effect of any clock jitter going into the ADC gets multiplied by the 900/5, so at some point obtaining a decent oscillator becomes impractically expensive. ---Joel |
#163
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Wind/Solar Electrics ???
"SolarFlare" wrote in message
... Now you have to provide samples ***AND*** changing information with an algorthm to decode successfully. Your samples are then not complete and useless without other information supplied. This is true, but it's pretty much true for all communication systems, not just sub-sampled digital ones. What changes is that sometimes the extra 'information' supplied can be done by something as sophisticated as a human's brain as he tunes across the dial to find the 'best' sound -- this corresponding to finding the carrier. (At some point this becomes a very philosophical discussion... 'information' only has _meaning_ to an observer who presumably knows something about or has a hunch as to what they're observing is. Although one can compute the 'information' within signal in an attempt to ascertain whether it resembles a random process or whether it's conveying what we may 'intelligence.' Hence you can probably recognize the difference between someone speaking random jibberish and an actual language even without knowing that language, but on the other hand a good way to conceal information is to make it appear almost completely random -- when in fact it isn't --, which is exactly what cryptography does.) Let's see you regenerate the original carrier and information from that without the carrier frequency known. Example: Take an antenna that's about a meter long... feed its output to an LNA and then a reasonably steep bandpass filter passing 144-148MHz... sample with a 16 bit, 12MSps ADC (I chose 12 just because it shifts 144MHz to baseband, although there's no reason you can't use any frequency 8Msps). Feed this digital word to a 16 bit DAC clocked at 10MSps. Lowpass filter the DAC's output with a reasonably steep 4MHz low-pass filter. Feed this signal to one port of a mixer and 144MHz to the other port. Poof! There's your original signal back again! Feed this through another 144-148MHz bandpass filter if you don't like the image response at 140-144MHz. There are a few caveats he 1) Clock jitter will tend to broaden out the specctra of the original signals a bit (how good is your clock?) 2) The track & hold (analog) circuitry in the ADC has to be good to a couple hundred MHz to avoid distortion. 3) Your noise floor is limited to no better than ~-100dB (and potentially _much_ worse if you haven't been careful in your layout, power supply decoupling, etc.). Note that everything described above also applies to switched capacitor circuits (a technology whose time has just about passed, but a neat idea); in that case analog noise rather than quantization noise will dictate the noise floor (and realistically it'll probably be much worse than -100dB...) 4) A typical DAC holds its output (e.g., a first-order hold) rather than generating impulses, so the spectrum reproduced has a sin(x)/x profile to it (frequencies closer to 148MHz will have less gain than those at 144MHz); this can be fixed in the digital domain with the use of a FIR or IIR filter. In some systems the droop is small enough that people just ignore it. This example is reasonably practical. Strictly speaking, to make it simlper you can just bandpass filter the output of the DAC directly and be OK, but the sin(x) profile along with the limited analog bandwidth of the DAC tend to make this approach impractical (you end up with very little SNR); this approach if often used for proof-of-concept demos, though. If you happen to have a carrier at 146.23MHz in the input signal, it'll most certainly still be there in the output signal, yet the system didn't have to 'know' where the carrier was. When you listen to the audio on your radio can you tell the carrier frequency without the dial? Sure, I can measure it! In fact, a much more interesting problem is how one generates a carrier when none exists in the first place. There are plenty of modulation schemes out there specifically don't use a carrier to either save power (TV transmissions -- which have a very small albeit not eliminated carrier -- are a good example of this) or to conceal transmissions (in military systems nothing attracts unwanted attention more than a carrier some 60dB above the noise floor). ---Joel |
#164
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Wind/Solar Electrics ???
daestrom wrote:
So what you're saying is, *if* you know the carrier frequency and band-width of the signal imposed on that carrier, you can design a system that will be able to reproduce the imposed signal using a relatively low sample rate (low when compared to the carrier frequency). But if the carrier frequency changes, then you need to modify the sample rate to avoid a lot of aliasing issues. So in radio reception, the sample rate is adjusted along with tuning the receiver? Or is this done at the intermediate frequency which is fixed so that sample rate adjustment is fixed with the intermediate frequency? (do they even still use superheterodyning in tuners?? ;-) It's been a long time since I did any RF stuff. But A/D and D/A stuff at AF and lower has been quite a passion for me for some time. And the basic Nyquist hasn't changed. daestrom The carrier frequency has nothing to do with it. What is important is the bandwidth and the center frequency of the pass-band. Note that your signal needn't take up the whole bandwidth, and in a typical radio system the signal you are tuning to is a very small fraction of the pass-band. In any case, the pass band is defined by the anti-alias filter, so practically speaking, it is a fixed, known pass band. Therefore your *if* is satisfied. What subsampling buys you is a way to sample an IF that is at a higher frequency than the sample rate of your system, which may be limited either by the ADC or by your computational power. BTW, I never said nyquist changed. I was simply stating that it is more general than the commonly held belief that the sample rate has to be at least 2x the highest frequency. The truth is, the sample rate has to be at least 2x the bandwidth of the signal. |
#165
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Wind/Solar Electrics ???
SolarFlare wrote:
OK let's go with your analogy example of 1234 being represnted by 234 only. You have no way of decoding 234 into 1234 without passing information of 1000 as your baseband info and therefore the the number 1234 has not been successfuly representedm as being reproduced without further information. Now we could further argue algorythms as part of the information or part of the sample. Likewise, you have no way of discerning 234 is actually 234 and not 1234 with a 3 digit decimal number system. The problem is not unique to sub-sampling, it exists at baseband as well. The only difference is that at baseband the representation looks the same as the signal. In either case, you need to know the fixed constraints of the system to fully comprehend the meaning of the representation. For example, in a 3 decimal digit system, you have no way of knowing that 234 really is 234 and not 1234 or 2234 unless you also know that the inputs are limited to the range 0 to 999. The only way around that is to have an infinite number of "symbols" to represent all the possible data when the set of possible data is infinite. As soon as that set is not infinite, we can take advantage of our knowledge of the system to reduce the set of symbols to a manageable number of elements. I'd argue that any engineering requires a set of implied constraints in order to make the problem solvable. In the case of the subsampling, we know by design what the pass-band of the anti-alias filter is. That is a constant parameter designed into the system, so presumably it is know to designers of all the components of the system. In the example case, then, we set as a system constraint the fact that all inputs are in the range of 1000 to 1234. That constraint is a constant, and is implied by the design. No information is lost by not transmitting the constant that is already known throughout the system. Doing so simply wastes bandwidth on your communications channel. |
#166
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Wind/Solar Electrics ???
"Ray Andraka" wrote in message news:wZctf.58905$4l5.50283@dukeread05... daestrom wrote: So what you're saying is, *if* you know the carrier frequency and band-width of the signal imposed on that carrier, you can design a system that will be able to reproduce the imposed signal using a relatively low sample rate (low when compared to the carrier frequency). But if the carrier frequency changes, then you need to modify the sample rate to avoid a lot of aliasing issues. So in radio reception, the sample rate is adjusted along with tuning the receiver? Or is this done at the intermediate frequency which is fixed so that sample rate adjustment is fixed with the intermediate frequency? (do they even still use superheterodyning in tuners?? ;-) It's been a long time since I did any RF stuff. But A/D and D/A stuff at AF and lower has been quite a passion for me for some time. And the basic Nyquist hasn't changed. daestrom The carrier frequency has nothing to do with it. What is important is the bandwidth and the center frequency of the pass-band. Note that your signal needn't take up the whole bandwidth, and in a typical radio system the signal you are tuning to is a very small fraction of the pass-band. In any case, the pass band is defined by the anti-alias filter, so practically speaking, it is a fixed, known pass band. Therefore your *if* is satisfied. What subsampling buys you is a way to sample an IF that is at a higher frequency than the sample rate of your system, which may be limited either by the ADC or by your computational power. BTW, I never said nyquist changed. I was simply stating that it is more general than the commonly held belief that the sample rate has to be at least 2x the highest frequency. The truth is, the sample rate has to be at least 2x the bandwidth of the signal. After proper filtering of the input. |
#167
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Wind/Solar Electrics ???
You still had to supply the constraints so the sampling
is not complete for any waveform. This is like supplying $234 to buy that big screen TV when you have to supply $1000 under the table to actualy get it delivered. All the money is not upfront and the $234 is a lie. "Ray Andraka" wrote in message news:2gdtf.58906$4l5.30943@dukeread05... SolarFlare wrote: OK let's go with your analogy example of 1234 being represnted by 234 only. You have no way of decoding 234 into 1234 without passing information of 1000 as your baseband info and therefore the the number 1234 has not been successfuly representedm as being reproduced without further information. Now we could further argue algorythms as part of the information or part of the sample. Likewise, you have no way of discerning 234 is actually 234 and not 1234 with a 3 digit decimal number system. The problem is not unique to sub-sampling, it exists at baseband as well. The only difference is that at baseband the representation looks the same as the signal. In either case, you need to know the fixed constraints of the system to fully comprehend the meaning of the representation. For example, in a 3 decimal digit system, you have no way of knowing that 234 really is 234 and not 1234 or 2234 unless you also know that the inputs are limited to the range 0 to 999. The only way around that is to have an infinite number of "symbols" to represent all the possible data when the set of possible data is infinite. As soon as that set is not infinite, we can take advantage of our knowledge of the system to reduce the set of symbols to a manageable number of elements. I'd argue that any engineering requires a set of implied constraints in order to make the problem solvable. In the case of the subsampling, we know by design what the pass-band of the anti-alias filter is. That is a constant parameter designed into the system, so presumably it is know to designers of all the components of the system. In the example case, then, we set as a system constraint the fact that all inputs are in the range of 1000 to 1234. That constraint is a constant, and is implied by the design. No information is lost by not transmitting the constant that is already known throughout the system. Doing so simply wastes bandwidth on your communications channel. |
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