Wind/Solar Electrics ???

"Ray Andraka" wrote in message
news:C7nsf.35562$Mi5.29016@dukeread07...
daestrom wrote:
"Ray Andraka" wrote in message
news:0Gdsf.34358$Mi5.34121@dukeread07...

daestrom wrote:

So, if I have a signal with a 1000 hz carrier, with a bandwidth of 50
hz, you think I can sample it at just 150 hz and get accurate
reproduction? That's just wrong.

It is the maximum frequency component in the signal that is important.
The bandwidth is not related unless the lower edge of the band is at 0
hz (whereupon the upper side of the band is equal to the max frequency).

daestrom



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.


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



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.

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

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.

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

"daestrom" wrote in message
...
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).

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.

But if the carrier frequency changes, then you need to modify the sample
rate to avoid a lot of aliasing issues.

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.

So in radio reception, the sample rate is adjusted along with tuning the
receiver?

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.)

Or is this done at the intermediate frequency which is fixed so that sample
rate adjustment is fixed with the intermediate frequency?

This is quite common.

(do they even still use superheterodyning in tuners?? ;-)

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

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

"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

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.

"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.