Questions about equivalents of audio/video and digital/analog.

[Bob Myers]

Sampled analog systems are certainly
not very common today (unless you count certain forms of
modulation as "sampling," and in fact there are some very close
parallels there), but the theory remains the same no matter which
form of encoding is used. In any event, you must sample the
original signal at a rate equal to at least twice its bandwidth
(actually,
very slightly higher, to avoid a particular degenerate case which
could occur at EXACTLY 2X the bandwidth) in order to preserve
the information in the original and avoid "aliasing."

Is the CCD [Charge Coupled Device] a "sampled analog system"?

It's certainly one example of such, being essentially an
analog shift register.

Bob M.

 

[Jerry Avins]

If you quantize the magnitude, it is digital. That is
by definition.

I believe that the definition is flawed. Not that it matters; it's good
enough in context. A signal can be quantized without any need to measure
it or describe it with a number. An example is the signal being measured
in a quantum Hall-effect experiment.

Jerry

 

[Bob Myers]

"Digital" and "subject to aliasing" are two different things.

As I believe the term "digital" is usually meant, it implies a
two-state (on/off) storage representation.

Not necessarily; a two-state representation is most properly
referred to as "binary." The best definition of "digital" I've
managed to come up with comes in the word itself - it
is the encoding system whereby information is stored as
"digits," i.e., numeric values, as opposed to a system in which
the information is stored "analogously" in the form of one
parameter (voltage, say) which varies in a like manner as the
original.

"Quantized" and "sampled" are terms which are really not all
that closely associated (at least in theory) with either of the
above, although admittedly most systems seen today which
employ sampling and/or quantization are also "digital" in the
nature of the encoding of the information carried.

Bob M.

 

[Randy Yates]

[...]

A "quantized analogue signal" is digital by definition.

No, you haven't. You merely have a signal at a set of discrete levels.
You need an analogue to digital converter to take each of those
quantized levels and convert it into a digital word (of 1s and 0s).

Digital means "represented by digits", not "in discrete voltage
steps".

I've never seen that definition, while I have seen the definition
Floyd is proposing, and I think it is a reasonable one.

I've also seen many contexts in which "digital" means "discrete-time,"
i.e., there is no amplitude quantization at all. Take for example any
of a number of books on the subject which have "digital signal
processing" in the title - they are referring to signals that have
been sampled in time, but not quantized (generally, although
quantization effects are also analyzed in several such texts).

Do you have a reference for your definition?
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% <[email protected]> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

 

[Bob Myers]

analogue - a continuous representation of the original signal

A CCD is an example of a device which stores information
in an analog manner, but non-continuously.

Bob M.

 

[Bob Myers]

It makes no difference how the levels are represented.

Sure it does. If the levels of the original signal (or rather,
whatever parameter of the original information is being
recorded/stored/process are represented by analogous
levels of some other parameter (e.g., sound represented
by voltage), then the system is "analog." It is certainly
possible to conceive of a quantized analog system, although
such things are rarely if ever seen in practice.

"Analog" also does not imply "infinite" precision or
adjustability, since, as is the case in ALL systems, the achievable
precision (and thus the information capacity) is ultimately limited
by noise. See the Gospel According to St. Shannon for
further details...;-)

Bob M.

 

[Bob Myers]

A "quantized analogue signal" is digital by definition.

No, Don had it right. A quantized analog signal
remains analog as long as the relative values of the
quantization levels, one to the other have significance;
they thus can carry information, which is the fundamental
goal of any such system.

Now, we could certainly assign values to those levels
which (for instance) are NOT in order from "top to
bottom" (or whichever direction you choose to use),
which might be done to distribute the susceptibility of
any given "bit" in said value to noise evenly. In this
case, the levels MUST be interpreted as the intended
numeric values in order to recover the original
information, and hence this would be a "digital"
encoding system.

QUANTIZATION:
A process in which the continuous range of values
of an analog signal is sampled and divided into
nonoverlapping (but not necessarily equal)
subranges, and *a* *discrete*, *unique* *value* *is*
*assigned* to each subrange.

http://ntia.its.bldrdoc.gov/fs-1037/

Exactly. But mere quantization by itself does not
suffice to render a signal "digitally encoded," no
matter what a given government "expert" may claim.

Bob M.

 

[Jerry Avins]

If you quantize it, you *have* assigned a value to it,
and that value is not from a continuous set, but from a
discrete finite set, and therefore it is digital.

A "quantized analogue signal" is digital by definition.

(Emphasis added)

QUANTIZATION:
A process in which the continuous range of values
of an analog signal is sampled and divided into
nonoverlapping (but not necessarily equal)
subranges, and *a* *discrete*, *unique* *value* *is*
*assigned* to each subrange.

http://ntia.its.bldrdoc.gov/fs-1037/

The government declares it so it must be true? I can demonstrate a
circuit using analog components that transforms a continuous ramp input
into a staircase output. Moreover, the output levels can be individually
adjusted. Is the output digital? (We're discussing an arbitrary
definition here. There is no wrong answer.)

Jerry

 

[Randy Yates]

[...]

A "quantized analogue signal" is digital by definition.

No, you haven't. You merely have a signal at a set of discrete levels.
You need an analogue to digital converter to take each of those
quantized levels and convert it into a digital word (of 1s and 0s).

Digital means "represented by digits", not "in discrete voltage
steps".

I've never seen that definition, while I have seen the definition
Floyd is proposing, and I think it is a reasonable one.

Let me back-pedal a little and say that, yeah, colloquially, digital
is related to "digits." But the term "digital signal" as used in texts
and industry does not hold to this colloquial usage. That is, a signal
that is completely unquantized in amplitude and represented in base 10
as an element of the real numbers could well be called a digital
signal. The key property of such a signal is that it is *discrete-time*
(i.e., sampled in time).
--
% Randy Yates % "The dreamer, the unwoken fool -
%% Fuquay-Varina, NC % in dreams, no pain will kiss the brow..."
%%% 919-577-9882 %
%%%% <[email protected]> % 'Eldorado Overture', *Eldorado*, ELO
http://home.earthlink.net/~yatescr

 

[Don Pearce]

[...]

A "quantized analogue signal" is digital by definition.

No, you haven't. You merely have a signal at a set of discrete levels.
You need an analogue to digital converter to take each of those
quantized levels and convert it into a digital word (of 1s and 0s).

Digital means "represented by digits", not "in discrete voltage
steps".

I've never seen that definition, while I have seen the definition
Floyd is proposing, and I think it is a reasonable one.

No, it isn't. It misses the fact that sampled and digital are
different things. Digits are numbers.

I've also seen many contexts in which "digital" means "discrete-time,"
i.e., there is no amplitude quantization at all. Take for example any
of a number of books on the subject which have "digital signal
processing" in the title - they are referring to signals that have
been sampled in time, but not quantized (generally, although
quantization effects are also analyzed in several such texts).

Really? Can you point me at something that does DSP on signals that
have been merely sampled in time? I've never come across any such
thing.

Do you have a reference for your definition?

Logic will do. If you are doing digital signal processing, you are
doing arithmetic on the numbers that come out of an AtoD converter.
You can't do that with some voltage levels out of a quantizer.

As for discrete time, that is simply sampled, like a class D
amplifier, and nothing to do with digits. There is plenty of laziness
in the use of nomenclature (as well as misuse by people who simply
have no idea what they are talking about).

d

 

[Bob Myers]

The purpose of this visual "pitch-shifting" is like a way to record/
playback/transmit/receive/store supreme-quality video while using the
least bandwidth and storage space necessary when low-pass filtering is
not an option.

And as you have been told countless times before, you REALLY
need to read up on the basics of compression, and specifically
the differences between "lossy" and "lossless" compression, and
what forces the differences between these two and what enables
the latter. Until you do, you'll never really understand any of
this.

Hence, if you want to get decent imagery in a low-bandwidth imaging
device, your best bet is to decrease the spatial frequency because
transferring it into the imaging device.

Or use fewer bits per sample, or just fewer bits for certain parts
of the information you're trying to capture (for instance, chroma
information vs. luma), or remove redundant information. (Think
about this: how efficient is it, if we have a section of an image which
is just a blank white area, to have each and every pixel there carry
information that equates to "I'm white!" "So am I!" "So am I"....
and so forth? Just one example to consider...). You can also
reduce the temporal frequency in the case of motion video. And
these are just the simpler approaches.

Bob M.

 

[Don Pearce]

[...]
A "quantized analogue signal" is digital by definition.


No, you haven't. You merely have a signal at a set of discrete levels.
You need an analogue to digital converter to take each of those
quantized levels and convert it into a digital word (of 1s and 0s).

Digital means "represented by digits", not "in discrete voltage
steps".

I've never seen that definition, while I have seen the definition
Floyd is proposing, and I think it is a reasonable one.

Let me back-pedal a little and say that, yeah, colloquially, digital
is related to "digits." But the term "digital signal" as used in texts
and industry does not hold to this colloquial usage. That is, a signal
that is completely unquantized in amplitude and represented in base 10
as an element of the real numbers could well be called a digital
signal. The key property of such a signal is that it is *discrete-time*
(i.e., sampled in time).

Sorry, but that is simply nonsense. A signal that is sampled in time,
but not quantized is an analogue signal. It is treated and processed
by analogue circuits. For a signal to be digital its sampled levels
must be represented by numbers, which are processed mathematically by
some sort of microprocessor. The signal can be reconverted to an
analogue one later by a D to A. The output of a D to A is still a
time-sampled signal, but since it is now a set of varying levels, we
again call it an analogue signal.

d

 

[Randy Yates]

[...]
A "quantized analogue signal" is digital by definition.


No, you haven't. You merely have a signal at a set of discrete levels.
You need an analogue to digital converter to take each of those
quantized levels and convert it into a digital word (of 1s and 0s).

Digital means "represented by digits", not "in discrete voltage
steps".

I've never seen that definition, while I have seen the definition
Floyd is proposing, and I think it is a reasonable one.

No, it isn't. It misses the fact that sampled and digital are
different things. Digits are numbers.

It isn't reaonable to you. Don't publish opinion as fact.

Really? Can you point me at something that does DSP on signals that
have been merely sampled in time? I've never come across any such
thing.

You haven't looked very far. Here is an example (a power calculation):

Px = \sum_{n=-\infty}^{+\infty} x^2[n],

where x[n] \in \R.

Logic will do. If you are doing digital signal processing, you are
doing arithmetic on the numbers that come out of an AtoD converter.
You can't do that with some voltage levels out of a quantizer.

As for discrete time, that is simply sampled, like a class D
amplifier, and nothing to do with digits. There is plenty of laziness
in the use of nomenclature (as well as misuse by people who simply
have no idea what they are talking about).

I won't argue that the current usage isn't good nomenclature, but that's
the way historically things have developed.
--
% Randy Yates % "Though you ride on the wheels of tomorrow,
%% Fuquay-Varina, NC % you still wander the fields of your
%%% 919-577-9882 % sorrow."
%%%% <[email protected]> % '21st Century Man', *Time*, ELO
http://home.earthlink.net/~yatescr

 

[Jerry Avins]

Doug McDonald wrote:

... It's very hard to STORE signals purely analog without
moving parts. In fact, I had a hard time thinking of any such
device that is or was purely analog. However, the old analog
storage oscilloscopes would meet your criteria if you don't
include electrons in a vacuum as moving parts. There the limit to the
frequency response is the size of the focus spot .... i.e.
the quality of the lenses! (Such device of course uses analog
electron lenses). If you don't intend to store forever, there
were things like analog mercury delay lines which stored signals
as sound waves travelling through mercury.

I mentioned mercury delay lines in an earlier post that probably hadn't
seen when you wrote that. There's another way that uses only common
electrical components -- capacitors and inductors. Cascaded low-pass T
(or pi) sections approximate a transmission line very well up to a
frequency determined by the product of 1/LC, while the characteristic
impedance is sqrt(L/C). Such "synthetic lines" were staples in telephone
research labs. The Bell Labs exhibit at the 1939-40 Worlds Fair included
such a line driven by a microphone into which a visitor could speak,
feeding headphones (s)he wore while speaking. Most visitors were reduced
to stammering by the delay, which I'm guessing was about two seconds; my
memory on that point is hazy. I impressed my parents (much like Radium
probably impressed his) by doggedly ignoring the feedback and speaking
clearly and deliberately. The demonstrator, a Bell Labs researcher,
asked us to wait while he fetched his boss to show me off. I do remember
being told that delays up to ten seconds were feasible, but that long
delays allowed the brain to more easily decouple speech and hearing, so
they weren't used in the demo. Bossman showed us the closet where the
delay line was stored. The parts were housed in two large relay racks.

Jerry

 

[Jerry Avins]

... If you are doing digital signal processing, you are
doing arithmetic on the numbers that come out of an AtoD converter.
You can't do that with some voltage levels out of a quantizer.

Transversal and recursive filters and correlators have been built that
operate on unquantized samples. Fourier transforms have been "computed"
with lenses. Do you remember the early days of side-looking radar?

As for discrete time, that is simply sampled, like a class D
amplifier, and nothing to do with digits. There is plenty of laziness
in the use of nomenclature (as well as misuse by people who simply
have no idea what they are talking about).

Agreed. Sometimes I'm guilty of sloppiness. It's the flip side of
explanatory excess.

Jerry

 

[Nobody]

(snip)

I believe there is a device more like an analog RAM used for
sound recording in toys. One can record up to about a
minute of voice and replay it many times.

That's just normal (digital) RAM with an ADC and DAC.

 

[Nobody]

My reading of the possible systems goes like this.

analogue - a continuous representation of the original signal
sampled - a representation of the signal at discrete time points

Both of these are analogue; if you want to distinguish the first case, use
"continuous".

"Analogue" = "how much", "digital" = "how many".

quantized - a sampled signal, but with the possible levels constrained
to a limited set of values
digital - a quantized signal, with the individual levels represented
by numbers

These are the same thing. Digital values *can* be represented by numbers,
but in practice they're represented by physical quantities. You can
the states of binary logic as 0 and 1, but in practice they're
represented by voltages.

Aliasing is going to happen as soon as you move beyond the first line
of that list.

Yep; aliasing is a consequence of sampling, not quantisation.

It's the quantisation which makes something "digital".

 

[Don Pearce]

[email protected] (Don Pearce) writes:
[...]
A "quantized analogue signal" is digital by definition.


No, you haven't. You merely have a signal at a set of discrete levels.
You need an analogue to digital converter to take each of those
quantized levels and convert it into a digital word (of 1s and 0s).

Digital means "represented by digits", not "in discrete voltage
steps".

I've never seen that definition, while I have seen the definition
Floyd is proposing, and I think it is a reasonable one.

No, it isn't. It misses the fact that sampled and digital are
different things. Digits are numbers.

It isn't reaonable to you. Don't publish opinion as fact.

Really? Can you point me at something that does DSP on signals that
have been merely sampled in time? I've never come across any such
thing.

You haven't looked very far. Here is an example (a power calculation):

Px = \sum_{n=-\infty}^{+\infty} x^2[n],

where x[n] \in \R.

Sorry, but that isn't DSP, it is just calculating the power. Let me
put this very simply. If you have a quantized signal and you want to
make it twice as big, can you do that with an amplifier, or do you do
it mathematically? If the signal is quantized, an amplifier will do
it. If it is digitized it won't. You can amplify 0110111001 all you
like, you will still have 0110111001.

I won't argue that the current usage isn't good nomenclature, but that's
the way historically things have developed.

Current usage is just fine. A digital signal is one composed of
digits.

d

 

[Don Pearce]

Transversal and recursive filters and correlators have been built that
operate on unquantized samples. Fourier transforms have been "computed"
with lenses. Do you remember the early days of side-looking radar?

Quantization isn't important. If you don't quantize all it means is
that you are dealing with floating point rather than integer numbers.
Still digital of course. I can't think of any floating point ADC's off
hand, of course.

Agreed. Sometimes I'm guilty of sloppiness. It's the flip side of
explanatory excess.

Jerry

We're all guilty of sloppiness. What is important is that we are able
to understand and work with the fine differences when they matter.

d

 

[Nobody]

No, you haven't. You merely have a signal at a set of discrete levels.

Those discrete levels *are* digits.

You need an analogue to digital converter to take each of those
quantized levels and convert it into a digital word

The circuit which performs the quantisation *is* an analogue to digital
converter.

Note that an analogue circuit with a "step" transfer curve
(e.g. a comparator) doesn't necessarily perform "quantisation". Whether or
not quantisation occurs is conceptual, and depends upon context (i.e. how
you intend to use that signal).

(of 1s and 0s).

Although binary is the most common base for digital systems, any base is
possible.

Digital means "represented by digits", not "in discrete voltage
steps".

The concept of "digit" is more general than you realise.

In essence, if you have a signal where the exact value (voltage etc)
doesn't matter, only the "category" (e.g. voltage band) in which it falls,
then it's digital, regardless of whether you have 2 categories or 10 or
100.

An important property of practical digital components is that they
regenerate the signal. If you define e.g. the range 0V-2V as "zero" and
3V-5V as "one", then each component will accept outputs which are near the
edges of the range and produce outputs which are further from the edges
(i.e. less ambiguous).

This property allows you to connect components together into arbitrarily
complex circuits without imposing extremely low tolerances on the inputs.

Moreover, it also allows the construction of feedback loops (sequential
logic), where a signal has to pass through an infinite number of
components (it passes through a finite number of components infinitely
many times).