Sampling without PAM, PWM, carrier signals, or modulation -- Analog Electronic Chip

Okay so sampling is a *must*. But can this sampling be done without
using PAM, PWM, or any carrier waves? Can't the charges be sampled in
the capacitors without adding any sort of modulation to them? If not,
they why?

 

Sorry I'd didn't understand what you just wrote.

 

No, per the Einstein-Feldburg equations, sampled charges
must be modulated through a transfinite hyperconductive
infidebulum matrix, with the resulting para-stable phase
incoherency reduced through application of the usual methods,
including negative beta-state feedback or loosely-coupled
ferro-optical heterodyne coils. The more astute reader will
note the latter can, at least potentially, produce undesirable
endochronic states and in extreme cases distortion of the
transconductive slew-rate limited noise figures, but in practice
these are of low enough vector magnitude in the frequency
domain so as to be ignorable.

Unless, of course, you've got a cold solder joint in there
somewhere.

Bob M.

 

Huh? Whatever are you going on about *now*? PAM, PWM, and
carrier waves have *NOTHING WHATSOEVER* to do with sampling.


Bob Masta

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Signal Generator
Science with your sound card!

 

---
As Bob Masta said: "Huh? Whatever are you going on about *now*?"

Here's what sampling is: Let's say that you have a 1000Hz 1VPP sine
wave of which you want to store one cycle and that you've got 360
capacitors on hand.

Then you might do something like this:

A B
ACIN>--O--> | <---------------------->OUT
| S2 1
S1 O---O--->O----------+
C C |
2 O------+ [C1]
. | |
. [C2] |
. | |
360 O--+ | |
| | |
[C360] | |
| | |
GND>--------------------+---+---+---->GND

S1 is a SPDT center-off analog switch of some kind and S2 is a 360
channel break-before-make analog switch. In order to store the
waveform what you do is start with S2 in position 1, very briefly
connect S1C to S1A, then return S1 to the OFF position. This will
charge C1 (Which is a tiny sample-and-hold cap) up to the voltage
of the input signal, more or less.

Once that's done, S2C is connected to S2-2 and the input signal
sampled again.

After 360 samples have been taken, S2 is is placed in the '1'
position, S2 is placed in the 'B' position, and S1 made to traverse
S1-1 through S1-360 at the same rate as when the samples were taken.

When that's done, the voltages each capacitor has been charged to
will be presented at "OUT" sequentially, recreating the input
waveform with only very light low pass filtering required between
the different output samples.

What I've shown you is _very_ rudimentary, and there needs to be a
mechanism employed to discharge the caps, which I haven't shown, but
which I'm sure you can find if you Google "sample and hold"

 

Perhaps you should do some more research in this field,
then.

Bob M.

 

Thanks for clearing that up.

 

Thanks for the illustration.

Why is sampling required before digitizing a signal?

 

Strictly speaking, though, it isn't really mandatory that the
sampling process come first. One could easily devise a "continuous"
sort of A/D (just a string of resistors and some comparators
should do the trick) from which the digital values could then
be sampled at regular intervals. There are, of course, practical
reasons for putting a sample-and-hold in there first, but in
theory the process works just the same either way.

What IS required, of course, is bandlimiting of the signal
prior to sampling...

Bob M.

 

How does one digitize a non- sample?

A sample is a sample regardless of the method. John did not say it had to
use a sample-and-hold process.

It's not mandatory if the sample rate is high enough.

 

The situation described would have N bits of output
from the continuous A -> D function, which would be
changing without any particular relationship to one
another in time. Admittedly, you would have to sample
(e.g., capture the value via a clocked register) to make
much sense of it (particularly if it was changing quickly
enough! ).

There's still no sampling going on in the above example PRIOR
to the output's state at a given instant being captured in a register.
Quantization, yes, but not sampling.

Unless the sampling rate is infinite - which has proven to
be difficult to achieve in practical designs - the bandwidth
of the input signal MUST be strictly limited to less than 1/2
the sample rate in order to avoid aliasing, per the Gospel
According to St. Nyquist.

Bob M.

 

As I inferred in my comment, the sampling rate can be much greater than the
minimum required to meet the Nyquist requirement.

 

Assuming you mean "implied" - of course. But there's
still a requirement that the input be bandlimited. If you
can count on the input being well below 1/2 the sampling
rate, which is what I INFER you mean, then that
requirement is already met, right?

Bob M.

 

The band-limiting Bob Meyers is referring to is a function
of sample rate... you need to limit the band to less than
half the sample rate.

The string-of-comparators A/D is a typical "flash" converter
approach, used where speed is more important than resolution.
(You almost never see these with more than 8 bits, since that
requires 255 comparators.) Their conversion rate is limited by
the settling time of all the comparators, but they often go into
the 10s or 100s of MHz. In principle, they would be "continuous"
if they had infinitely-fast comparators. This is a separate issue
from the sampling process, which has to do with when and how often
you *read* those comparators.

There is also a clever (but not terribly useful) continuous conversion
design that only has one stage per bit, and can be cascaded for more
bits. It involves determining whether the incoming signal is above
or below half of full-scale, and subtracting off that half if so,
before passing the signal to the next stage. But this is even harder
to do quickly, and hard to make accurate, so it's not used as a
stand-alone converter. But the basic concept is sometimes used
as a front end, to handle a few bits of pre-conversion ranging, etc.

Best regards,




Bob Masta

D A Q A R T A
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Signal Generator
Science with your sound card!

 

You infer correctly.

Don