Wind/Solar Electrics ???

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.

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.

SolarFlare wrote:

If only the baseband frequency is sampled at 6kHz then
information is missing to recreate the original 100kHz
and the sampling information is insufficient to
recreate the original signal.


This is analogous to saying the number 1234 can be
represented by
(1234-234) / 1000 = 1

If I supply the number 1.0 you can regenerate the
number 1234 from it? Not true, without the rest of the
sampling information. The sample is incomplete.

Bandwidth sampling only cannot recreate the original
signal.


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.

"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

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.

wrote:
George Ghio wrote:

wrote:

George Ghio wrote:


I did build a kit inverter, once, years ago. It had a max rating of
150W, Which it met.

It had a half hour rating of 0W

And a surge of about 300W


I'm still scratching my head over that one.


Which part don't you understand


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


NT

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. 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.

George Ghio wrote:
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.

wrote:

George Ghio wrote:

wrote:

George Ghio wrote:



I did build a kit inverter, once, years ago. It had a max rating of
150W, Which it met.

It had a half hour rating of 0W

And a surge of about 300W



I'm still scratching my head over that one.



Which part don't you understand



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


NT

"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

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.


"Ray Andraka" wrote in message
news:WUdsf.34360$Mi5.17847@dukeread07...
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.