[William Sommerwerck]

I recently wrote a highly negative Amazon review of a book on signal
analysis. I received this comment from someone named Justin Lis.

"Just pointing this out there, but it is impossible to have an analog signal
that is discrete time. An analog signal can be represented by a discrete
time signal very well, but an analog signal IS continuous, where a discrete
time signal is defined as being discontinuous. Since it is impossible to
have a continuous signal be equal to a discontinuous signal, your argument
is invalid."

This is, of course, completely incorrect. If you believe it's correct, you
need to study the sampling theorem, and a few other things. In particular,
you need to understand why time sampling is not the same as amplitude
sampling (quantization).

Do you understand why I'm constantly griping that people don't what they
hell
they're talking about?


--
"We already know the answers -- we just haven't asked the right
questions." -- Edwin Land

[Mark]

On Sep 11, 7:08*pm, "William Sommerwerck"
wrote:
I recently wrote a highly negative Amazon review of a book on signal
analysis. I received this comment from someone named Justin Lis.

"Just pointing this out there, but it is impossible to have an analog signal
that is discrete time. An analog signal can be represented by a discrete
time signal very well, but an analog signal IS continuous, where a discrete
time signal is defined as being discontinuous. Since it is impossible to
have a continuous signal be equal to a discontinuous signal, your argument
is invalid."

This is, of course, completely incorrect. If you believe it's correct, you
need to study the sampling theorem, and a few other things. In particular,
you need to understand why time sampling is not the same as amplitude
sampling (quantization).


an analog signal is continuous in time and in amplitude.

if you sample an analog signal you will have a signal that is still
continuous in amplitude (it can be any amplitude) but it is discrete
in time, i.e. it exists at only the sampling instants in time and
does not exist at other times. Think of a series of arrows, the arrows
can be any length. Most people would NOT call this signal analog but
it is also not (yet) digital.

you can then quantize this sampled signal in amplitude as well.
now the arrows can then be only certain lengths. Now it is digital.

you are correct that sampling and quantization are two separable
processes.

Mark

[Don Pearce[_3_]]

On Sun, 11 Sep 2011 18:58:22 -0700 (PDT), Mark
wrote:

On Sep 11, 7:08*pm, "William Sommerwerck"
wrote:
I recently wrote a highly negative Amazon review of a book on signal
analysis. I received this comment from someone named Justin Lis.

"Just pointing this out there, but it is impossible to have an analog signal
that is discrete time. An analog signal can be represented by a discrete
time signal very well, but an analog signal IS continuous, where a discrete
time signal is defined as being discontinuous. Since it is impossible to
have a continuous signal be equal to a discontinuous signal, your argument
is invalid."

This is, of course, completely incorrect. If you believe it's correct, you
need to study the sampling theorem, and a few other things. In particular,
you need to understand why time sampling is not the same as amplitude
sampling (quantization).


an analog signal is continuous in time and in amplitude.

if you sample an analog signal you will have a signal that is still
continuous in amplitude (it can be any amplitude) but it is discrete
in time, i.e. it exists at only the sampling instants in time and
does not exist at other times. Think of a series of arrows, the arrows
can be any length. Most people would NOT call this signal analog but
it is also not (yet) digital.

you can then quantize this sampled signal in amplitude as well.
now the arrows can then be only certain lengths. Now it is digital.

you are correct that sampling and quantization are two separable
processes.

Mark

Not quite. Once you have sampled the signal it is necessarily discrete
in both amplitude and time (Both are stepped), even though the steps
can be of any amplitude. Once quantization has occurred, as you say,
the signal is of a limited set of lengths, but they are still lengths
and subject to the vagaries of the analogue circuit. Only once those
lengths have been measured, and represented by numbers (digits) is the
signal digital.

d

[William Sommerwerck]

"Mark" wrote in message
...

an analog signal is continuous in time and in amplitude.

if you sample an analog signal you will have a signal that is still
continuous in amplitude (it can be any amplitude) but it is discrete
in time, i.e. it exists at only the sampling instants in time and
does not exist at other times. Think of a series of arrows, the arrows
can be any length. Most people would NOT call this signal analog but
it is also not (yet) digital.


Perhaps the best thing for me to do is to find a large concrete wall and
bang my head against it until I pass out.

In a sampled signal, the original, unchanged "continuous" signal exists as a
component. I would suggest you get a copy of Lahti and read the chapter that
explains the sampling theorem, both mathematically and graphically. You may
draw your own conclusions.

[William Sommerwerck]

I'm one of those fortunate people blessed with Ausperger's syndrome. One of
its characteristics is the insistence on seeing things in terms of general
principles. This explains why "other people" too-often vehemently disagree
with me.

[Meindert Sprang]

"William Sommerwerck" wrote in message
...
I'm one of those fortunate people blessed with Ausperger's syndrome. One
of
its characteristics is the insistence on seeing things in terms of general
principles. This explains why "other people" too-often vehemently disagree
with me.

My son and I are also blessed with Asperger. What I've learned over the
years is to accept that others do not have this insistence to see things
this way and since I've stopped 'forcing' others to do so, I've made my life
a lot easier ;-)

Meindert

[Arny Krueger[_4_]]

"William Sommerwerck" wrote in message
...

I recently wrote a highly negative Amazon review of a book on signal
analysis. I received this comment from someone named Justin Lis.

"Just pointing this out there, but it is impossible to have an analog
signal
that is discrete time.

That begs the question of what do you call an analog signal that is sampled?
IOW, one that has been processed by a sample-and-hold?

An analog signal can be represented by a discrete
time signal very well, but an analog signal IS continuous, where a
discrete
time signal is defined as being discontinuous.

The corresponding statement for the same signal when it stays in the analog
domain is that an analog signal can be represented by another analog signal
very well, but the original signal has its exact value, while its analog
representation is always slightly different than the original signal.

"Exact" only exists in the digital domain.

"Exact" *never* exists in the analog domain. This may seem counter-intuitive
to some, but if you spend enough time working with some really good
measuring equipment you will find it to be true.

Since it is impossible to have a continuous signal be equal to a
discontinuous signal, your argument
is invalid."

Similarly, it is practically impossible for any analog signal that
represents another analog signal to be identical to it.

This is, of course, completely incorrect. If you believe it's correct, you
need to study the sampling theorem, and a few other things. In particular,
you need to understand why time sampling is not the same as amplitude
sampling (quantization).

In the end, a signal that is an exact replica of another signal would be
possible when both signals are in the digital domain.

Do you understand why I'm constantly griping that people don't what they
hell they're talking about?

It's all about whose hair is being split! ;-)

The point of all my nit picking about analog signals is that today, we often
have signals that have been round-tripped through the digital domain with
all of the approximations and estimations that people like to split hairs
about, and they are more exact copies of the origional signal than would be
possible if the signal had stayed in the analog domain.

[hank alrich]

Arny Krueger wrote:

"Exact" *never* exists in the analog domain. This may seem counter-intuitive
to some, but if you spend enough time working with some really good
measuring equipment you will find it to be true.

Heisenberg. In the digital world time stands still.

--
shut up and play your guitar * http://hankalrich.com/
http://www.youtube.com/walkinaymusic
http://www.sonicbids.com/HankandShaidri

[timewarp2008]

You can represent an analog audio signal on the X-Y plane, with the
X-axis (the domain) representing time, and the Y-axis (the range)
representing voltage, air pressure, cone displacement, or the like.
The signal is a continuous function, but mathematically, it can be
discontinuous, even if it's not "discrete time." In the real world,
however, this isn't going to happen. The speaker cone won't go
from -2.3 mm to +4.0 mm without passing through the continuum
of values between.

When you sample the signal, yielding a "discrete time" signal, you
no longer have a continuous curve in time. The only X-axis values
that have Y values are members of the set of sample times, and
there are no Y-axis values for other values of X. The signal is not a
continuous-time signal; it's discrete-time. But the Y values are no
longer continuous either. There is a discontinuity between each pair
of adjacent points. If you haven't quantized the signal, then the Y
values are not constrained to be discrete value (members of a finite
set of values). There can be any value. But that doesn't mean that the
values are continuous. They are discontinuous. In the time domain,
with real- world analog audio signals, the dichotomy "continuous
vs discrete" is essentially valid. But in the voltage range, it's not.
Allowing any voltage value doesn't make it continuous. It's clearly
discontinuous.

One of the fundamental misunderstandings here is the false
generalization
of the "continuous-time vs discrete-time on the time axis" dichotomy
to the false dichotomy of continuous-amplitude vs discrete-amplitude
on the voltage axis. The range of a function is not the same as the
domain. When you sample the signal at discrete times, not only does
the time-domain become non-continuous, so does the _function_ itself.
The output of a sample-and-hold function is not continuous in X or Y,
even before quantization.

A time-sampled signal is not continuous. Neither the domain nor
the range is continuous; the function itself is discontinuous. The
fact
that the range is not constrained to a finite set of discrete values
(i.e. that the amplitude values are not quantized) does not mean that
the amplitude values are continuous. The notion that a sampled
unquanized signal has "continuous" Y values is a fundamental
misunderstanding.

[Randy Yates]

On 09/12/2011 01:24 AM, Don Pearce wrote:
On Sun, 11 Sep 2011 18:58:22 -0700 (PDT),
wrote:

it is also not (yet) digital.

I propose that it is a matter of definition. Many DSP textbook presume
the "digital" signal has been quantized in time only.

Not quite. Once you have sampled the signal it is necessarily discrete
in both amplitude and time (Both are stepped),

Again, a matter of definition.

[gjsmo]

I would like to add another perspective, if I may. This is mainly
based on Calculus AB...
Specifically, a function (any function - audio is effectively a
function - call it a(t)) is continuous if:
1.) a(t) exists (is defined)
2.) The limit as t goes to x of a(t) exists
3.) These numbers are equal.

Therefore, for all purposes, signals created in the analog domain (and
measured in the analog domain) are continuous, since the signal is
always measurable (it exists, even if it's silence), the limit always
exists (audio can't go to infinity) and these numbers MUST be equal
(there are no discrete points which are not on the curve).
Purely digital signals are not continuous, since at every sampling
point, the limit is undefined - it is different from the left and
right sides. They cannot be defined by a function (unless it's a
piecewise function).

Thought I'd add a purely mathematical perspective. Feel free to argue
with me - I'm 16.