Wind/Solar Electrics ???

On Sun, 25 Dec 2005 17:50:50 +1100, George Ghio top-posted:

Just out of curiosity, is top-posting de rigeur on the rec.ovulation.awning NG? Someone has crossposted this to sci.erectionics. desire, and the convention there is to bottom- or mid- (or interspersed- ) post.

Just wondering - the clsoest I've been to aviating is I logged 4 hrs. worth of lessons in a C-150, and onec I sat in the Republic Airlines DC-9 simulator - that was a trip! My only other associations with aircarft other than as a passenter is that I worked at a place that sold little tiiny 28V 40A PSUs, and I'd rather jump out of an airplane (with a proper aprachute, of course), than try to land one. ;-)

Thanks! Rich

Which one do you have trouble reading?

the

to sci.erectionics.

mid- (or interspersed- )

I didnt seriously think you were going to stand by the above specs. Since you are, enough said.

NT

:) The trouble is he may actually BE a solar consultant. Nothing stopping him afaik. At least not for a few years anyway. :)

NT

No, it is correct. If you have a signal with a 1000 Hz carrier and a 50 Hz Bandwidth, you can indeed sample it at 150 Hz and get accurate reproduction...provided the rest of the spectrum is clear. That requirement is typically provided with an anti-alias filter. In this case, the anti-alias filter has to be a BAND-PASS filter centered on

1000 Hz rather than the low pass filter associated with baseband sampling. This works because sampling folds the spectrum (aliasing) so that parts of the frequency band with higher frequency than the sampling frequency get folded back onto baseband. As long as the full spectrum only has energy in a bandwidth less than or equal to half the sample rate, you get all of the information necessary to reconstruct the original signal (assuming you know the characteristics of the fixed anti-alias filter so that you know which image to select when you unfold the spectrum). If there was signal energy outside of the Fs/2 bandwidth, it adds to signal inside the bandwidth during the folding that sampling causes, and then you lose information since there is no way to separate the energy if it has been added with other energy by folding.

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.

You've used the wrong part of 1234 for your example. The proper analogy would be to say that 1234 can be represented by 234 in a 3 digit decimal number system. In that case, the overflow caused by exceeding 999 results in 1234 aliasing onto 234. If you know that all your input numbers are between 1000 and 1999, then 234 is sufficient information to represent 1234 with no ambiguity.

The anti-alias filter on your sampling system performs the bracketing to make sure that all the possible inputs are constrained to be within a bandwidth of your center frequency +/- BW/2, so when sampled there is no aliasing. In essence, that filter is the constraint that makes it work.

BTW, the same holds true for baseband sampling: The numbers in a baseband system based on your example are assumed to be less than 1000, so that 234 accurately represents 234. In that case if you put in 1234, it would also map to 234 and you'd have an ambiguity. It just so happens that in the baseband case, the representation is the same as the original signal for signals within the bandwidth allowed by Fs/2. With other than baseband, the representation is not the same as the number represented, but the constraints imposed by the system allow you to reconstruct the original value without ambiguity.

The information that tells you the frequency of the carrier is not discarded, but is partially implied by the system, just as it is with a baseband system. Remember, sampling is essentially the mixing of the signal with an impulse train, followed by a sample rate decimation without any filtering. The choice of frequencies in this example are unfortunate because there is in fact some interference between the positive and negative frequency images of the original signal. When dealing with real-only inputs, you need to be judicious in selecting the sample frequency so that the frequency folding does not fold the negative image (that is a reflection of the positive image and is always present for a real signal) onto the positive image. Still, that doesn't mean that the sample frequency has to be a sub-multiple of the carrier. For example, 160 Hz sampling works (as does 210 Hz) with a 1000Hz signal that has a 50Hz bandwidth because it puts both the positive and negative frequency images into the sampled spectrum without overlap. There is sufficient information there to reconstruct the original signal if the center frequency of the anti-alias filter is known.

And yes, you are correct that the sampled signal is indistinguishable from one which it aliases onto: but those other frequencies are not present in the signal thanks to the anti-alias filter. The point is that the anti-alias filter needn't be a low pass filter. It can be a band pass filter as long as the bandwidth is less than half the sample frequency. If the input signal is a real signal, there are additional considerations to make sure that the postive and negative frequeyncy images do not overlap when the spectrum is folded.

You are in effect demodulating the incoming signal and sampling the result, not sampling the incoming signal. You are 'throwing away' the information that would tell you what the carrier freq is.

Now, in radio that may be all well and good, since demodulation is a necessary part of reception anyway. But some of us were talking about reproducing the incoming signal, not stripping out the low freq component of some carrier.

Note that if the carrier is an exact multiple of the sample rate, *then* an unmodulated carrier will produce no 'alias' signal. But 150 doesn't go evenly into 1000.

If you have a completely unmodulated 1000 hz signal, passed through a 50 hz wide band-pass, centered around 1000 hz and sampled at 150 hz, your sampled data is indistinguisable from that of a 25 hz signal. Even knowing the band-pass filter's characteristic doesn't tell me if the carrier was unmodulated 1000 hz, or if there was a true 30 hz signal modulating it.

daestrom

Ah I see. Non compus mentis is your base state.

Let's See if we can clear up the story for you.

150W max continuous rating. Didn't think that would have been to hard to glean from the post if someone knew how inverters are rated.

0W half hour rating. That would indicate that the inverter in question does not, in fact, have a half hour rating.

300W surge.This means that the inverter will supply 300W for a couple of seconds or less. Enough to start a small motor or a TV.

Sorry you are TSP.

snipped-for-privacy@care2.com wrote:

It's a litle more general than that -- you only need to know that your signal lies inbetween some lower and upper frequencies and that bandwidth is (generally) less than 1/2 of the sample rate of the ADC.

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.

Not usually, although there are so many ways to build 'a radio,' I'm sure this approach has been implemented at some point in time.

It pretty common to digitize significantly more of a radio band than the bandwidth of the signal you're interested in and then just digitally track & demodulate the one signal you need from the many that are present. This is popular because none of the 'fundamental' settings of the system (local oscillator frequencies, IF frequencies, ADC sample rate, anti-alias filters, etc.) change; this makes the architecture inexpensive and highly flexible. The downside is that sensitivity can be poor if there are other, stronger sides in the band that you've digitized but aren't really interested in... A common fix for this problem is to stick an adjustable notch filter somewhere in the analog path, but of course that adds cost again... etc, etc, etc... we sit around all day making these tradeoffs. :-) Another common fix is to switch to frequency hopping spread spectrum modulation like Bluetooth uses. (From a certain point of view, people like the cell phone carriers have it easy in that they _own_ the spectrum they're operating in and know _exactly_ what signals should be present, their power levels, etc. -- That makes their radio designs noticeably simpler and cheaper than "general purpose" wideband receivers that are used by, e.g., the military, hams, etc.)

This is quite common.

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

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.)

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 here:

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.

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

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.

The proper analogy

in a 3 digit decimal

exceeding 999

all your input

sufficient information to

just

at > 2x the

filtered to energy

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?

whatever sideband(s) you care

you've lost nothing and

to an IF that can be

problem with trying to

5Msps ADC is that the effect

multiplied by the 900/5, so at

impractically expensive.

Actually, I kind of chose those numbers for that very reason ;-)

When

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.

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.