Wind/Solar Electrics ???

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.

"Me" wrote in message
...
In article
,
"daestrom"
wrote:

"Spehro Pefhany"
wrote in message
...
On Fri, 23 Dec 2005 18:46:49 GMT, the renowned
"daestrom"
wrote:


wrote in message
...
Joel Kolstad
wrote:

(I can't tell you how many times I've seen
people stating something
like,
'The Nyquist theorem requires sampling at at
least twice the highest
frequency present in the signal," when of
course it says no such thing.)

What do you think it means?


Nyquist figured out that higher frequency
components of the input signal
will 'alias' and you will lose the ability to
tell them from lower
frequency
components. In order to avoid 'losing
information' and not being able to
tell whether a particular sample stream was from
a low or high frequency
component, Nyquist's theorem states you must
sample at least twice as fast
as the highest component present.
snip

More than twice the bandwidth.



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



You are getting your terms confused here guys.
Nyquist requires that
you input both the Center Frequency, and Bandwidth
when determining
the Sampling Rate. If the sampling is done at
BaseBand then only the
Bandwidth is relevent. If the sampling is not done
at baseband, then
the Center Frequency, and Bandwidth are required to
determine samling
rate. Example, if the Bandwith of the signal is 3Kc
and the sampling is
done at BaseBand then sample rate needed would 6Kc.
If the sampling is
done at 100 Mhz with the same 3Kc bandwidth, then a
200.006 Mhz sampling
rate would be required.

It is much easyier to do DSP at baseBand, than at IF
Frequencies, and if
you do DSP at IF Frequencies, the lower the IF
Frequency, the easyier it
is to do, and the slower the DSP has to run.

Me

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.

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.

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.

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.