I thought to post this yesterday, but decided not to because much of it is
redundant to what has been discussed here lately, and it is long. However,
I've decided to post it now because Roy cites some DyR definitions from
audio that I think will help us move away from the fixation of bits that
seems to inexorably dominate when discussing scanners, even though we all
agree they are only a function of the digitization of a DyR.
(I find it fascinating how much we all agree on this then find a way to
discuss it again and again as though each time it were it were fresh and
illuminating. I'm convinced that NOT discussing bits is the key to moving
this conversation forward).
One last thing, we are all getting frustrated by the redundancy, but I'm not
convinced it's time to give up just yet. So, I'd like to advocate that those
of us who do choose to continue, try to keep it cool and cordial. If anyone
finds Roy's tone provocative at any point please remember this was written
in another place and time.
This was Roy's first post to the max-noise list:
------------------------
on 7/4/02 1:57 PM, Roy Harrington wrote:
Greetings All!
Since some of you may not know who I am, let's just say I am a concerned
participant in the issue of Dynamic Range. To date I've witnessed three
separate large discussion/ arguments about it with many hundreds of posts.
I was out of town for the latest one in the filmscanners group. I was an
active participant in the previous one in the digital BW yahoo group and saw
the tail end of one in the piezo BW yahoo group. In all three cases the
argument finally died leaving the participants totally frustrated and most
of the other group members very alienated. None of the discussions resulted
in an agreed upon resolution.
In this writing, my desire is to attempt to resolve this issue and forego
future non-productive arguments. I'm determined not to get into battle of
"Yes it is" <--> "No its not". This may be a difficult task but I feel
compelled to at least try. So here goes nothing :)
----------------------------
What I notice most about much of the discussion in the incessant wandering
of what the heck we're talking or arguing about. Its all based on Dynamic
Range but whether its audio, video, scanners, imaging, signal processing,
volt meters, etc. keeps the discussion from focusing on anything in
particular. I'd like to start off with a very specific reference and
situation.
The reference that was introduced by Austin and referenced repeatedly is
Higgins book "Digital Signal Processing in VLSI". I think everyone is
comfortable with this text and agrees with what is stated in it. The
section of interest is:
1.4.1 Dynamic Range Example: Analog Vs Digital Audio (I.e. this is mainly
written with audio in mind and I'd like to stay fixed in that context for
now. The both analog & digital are intertwined here but we can concentrate
on the analog).
The equation of interest is:
DynamicRange (db) = 20*log10 (largest/smallest discernible signal)
with signals expressed in voltage or current.
there's a footnote: decibel is defined as 10*log10(power ratio) power
versus voltage accounts for the extra power of 2.
The picture he shows is labeled as an analog vinyl record groove:
---------------------------- Austin's Statement
Here's Austin's statement about the text and diagram:
Austin wrote:
>Reference this diagram:
>
>
>
>"largest" is shown on this diagram to be the maximum signal level minus the
>minimum signal level, and is the largest range or absolute range that the
>signal can go from <=> to. Example, maximum signal level is 5, minimum
>signal level is 2, the absolute range/largest range is (5 - 2) or 3.
>
>"smallest" is shown as the noise. It is the same thing as "smallest
>discernable signal", which means the smallest change that can be detected.
>
>Where the signal is at it's lowest point, is what I am calling "minimum
>signal level".
>
>Where the signal is at it's highest point, is what I am calling "maximum
>signal level".
>
>The dynamic range equation is, using these terms, and the provided diagram,
>can be either of the following:
>
>DR (dB) = 10log10 (largest/smallest)
>
>DR (dB) = 10log10 ((maximum signal level - minimum signal level) / smallest)
>
>You can substitute "smallest DISCERNABLE signal" for "smallest" in these
>equations. Do NOT confuse "smallest"/"smallest discernable signal" with
>"minimum signal level", they are not the same thing, though in some
>circumstances they MAY have the same value.
>
First of all I'd like to commend Austin for his explicit statement of this
interpretation of the Higgins text. Its too bad that Higgins wasn't as
explicit about what he meant when he wrote the book. As the scan of the
diagram shows, the labeling of the diagram is fairly spare.
I'm quite sure that this is NOT the interpretation that Higgins had in mind
while writing the book. I'd like to be equally explicit about the correct
interpretation with supporting logic behind it.
------------------- Interpretation of Higgins text.
I'll begin with the fact that we're talking audio here. An "audio signal"
is a wave form not a single DC voltage. When you measure the size of an
audio signal what you measure is the amplitude of the wave form. In the
left half of the diagram we see an audio signal that spans the whole record
groove, the label "largest" is the amplitude of the largest possible wave
form i.e. amplitude of the largest possible signal or maximum audio signal.
The right half of the diagram shows a very small audio signal amplitude.
This term "smallest" or "smallest discernible signal" denotes the amplitude
of the smallest audio signal (a wave form) that is discernible above the
noise level. This might also be called the minimum audio signal.
So the ratio that you end up with is:
(amplitude of the max signal) / (amplitude of the min signal)
or in totality:
DynamicRange (db) = 20*log10((amplitude of the max signal) /
(amplitude of the min signal))
with audio signal measured in voltage.
As an aside the voltages can be measured peak-to-peak of the wave form or
using a AC volt meter that gives RMS (Root of the Mean Square) voltage. As
long as you us the same method in numerator and denominator the ratio is the
same.
What this gives you is simply the range of audio signal levels where the
audio system is operating within spec. In layman words, this is the
definition of dynamic range -- the range of audio output from softest to
loudest.
------------------------
This quite obviously is very different from Austin's interpretation. The
numbers may be close much of the time but getting the principles accurate is
crucial if we are to apply similar principles to completely other areas of
interest (not audio). Austin, you may now be thinking wrong, wrong, wrong
but ... please, please, please read what I am saying. Understand what I've
written first, don't merely deny it.
on 6/10/02 9:12 AM, Austin Franklin at darkroom@ix.netcom.com wrote:
> ... ... suffice to say, I am an
> authority on this subject, and a reasonably well known one within my field.
> I am happy to give my qualifications. What I've said is absolutely correct,
> and is the exact same understanding as other industry experts (not Photoshop
> gurus, and other authors who have never designed a bit of imaging equipment
> in their life, or ever software folks...many of these people also have
> proliferated this misunderstanding). If any of you know Kennedy McEwen (who
> is a far more well known expert than I am in this EXACT field), he and I
> have had many a discussion on this, and our understandings are precisely the
> same.
With statements like this there's certainly a large hurdle to clear. This is
NOT a battle of qualifications nor is it a battle of expertise. Its a issue
of what dynamic range is in the most general sense. I.e. not just digital
signal processing but all audio systems and ultimately all other phenomena
such as imaging.
I assume your field has to do with digital signal processing or something
close. When you digitize any signal you end up with discrete numbers and
discrete levels. The digital representation is designed to be a "good
enough" reproduction of the original using discrete levels. However, the
real analog signals have no discrete properties. They are completely
continuous. You are taking your knowledge of the discrete levels and
properties of digital processing and trying to shoehorn those ideas back
into the real, analog, continuous world. In your efforts to shoehorn
discrete levels back into the analog world you've taken a clearly analog
picture -- a groove of a vinyl record -- and attempted to assign discrete
levels where no such thing exists. Note, that I don't disagree with most of
the "rules of thumb" that you have stated as far as Dig Sig Proc, just that
they are artifacts of the DSP implementations and do not apply universally.
-------------------------
At this point I'd like to just go through various problems with your
interpretation and site references that agree with mine. This basically
boils down to what the preponderance of the evidence shows. I highly,
highly recommend printing out this whole post, taking it and the Higgins
book and discussing it with your friend Kennedy and any others whose opinion
you respect.
-------------------------
Back to your interpretation of the DynRange definition/formula. You are
transforming the denominator from "smallest discernible signal" into
"smallest discernible signal increment". The text makes no hint of
increment, difference, or anything of the sort. The noun in the denominator
is "signal", pure and simple, so you ought to be measuring a "signal" not a
difference or increment. The word "discernible" simply means detecting or
discerning signal above the noise, but you are turning it into
"distinguishability" of one level of signal from a different level of
signal, where that increment is the "noise" of the system. The very notion
of the existence of such an increment is impossible. This gets into the
exponential nature of audio. Suppose an amp that goes from 1 watt to 100
watts of output power. The power increment from 1 watt to 2 watts would be
easily distinguishable however going from 99 watts to 100 watts would be
impossible to distinguish. -- Basically, distinguishability is based on the
RATIO of the two wattages NOT the DIFFERENCE.
------------------------
Here's a web reference that YOU picked and said supported your case.
The first couple of paragraphs talk about DyR and number of bits in
agreement with much of your DSP statements. Further down though is the
equation for Dynamic Range. Have you checked it out?
DynamicRange = -20*log10 (noise level rms/maximum level rms)
The minus sign just flips the ratio. So "maximum level rms" corresponds to
"largest" -- and is NOT max - min. Also note the "rms" which you should
know is root mean square, exactly as I wrote above, and certainly implies
that "signal" means a AC audio signal.
------------------------ Supporting References
I spent a short time searching for "audio dynamic range" with google. This
is every definition of dynamic range that I found, not at all a select list:
Dynamic range describes the ratio of the softest sound to the loudest sound
in a musical instrument or piece of electronic equipment. This ratio is
measured in decibels (abbreviated as dB) units.
----
Dynamic range is the ratio of maximum undistorted signal (full-scale or
onset of clipping) to residual noise (noise floor). Dynamic range in
generally measured in decibels (dB).
-----
dynamic range -- the difference in loudness between the loudest peak and the
"noise floor" of your equipment.
-----
The dynamic range of an audio signal is the difference between the quietest
discernible part of the signal and the loudest undistorted part of the
signal. It is normally expressed in decibels (dB).
-----
This is a particularly nice one:
A short definition of dynamic range is probably in order at this point.
Dynamic Range (DR) as used in this paper is best described as the ratio of
the largest signal to the smallest signal in volts peak to peak, measured at
a given single frequency. The largest signal would be determined by applying
a signal to the unit and increasing the input to the unit until the unit's
specified total harmonic distortion (THD+N) is surpassed. The smallest
signal would be determined by applying a signal of the same frequency and
reducing the input until the output of the unit can no longer be
distinguished from the noise floor. This methodology works for either analog
or digital systems and by measuring either the input swing required or the
output swing given specifies input or output dynamic range (IDR or ODR)
respectively.
-----
Dynamic Range - 1) The level difference (in dB) between the loudest peak and
the softest level of a tune recording etc. 2) The level difference between
the level of clipping and the noise level in an audio device or channel.
Here's why we use the adjective "Dynamic":
Dynamics - 1) The amount of fluctuation in level of an audio signal. 2) In
music, the playing of instruments loudly or softly at different times.
------
dynamic range: The range between the loudest and the softest sounds that are
in a piece of music or that can be reproduced by a piece of audio equipment
without distortion. This is a ratio expressed in decibels (dB).
-------------------- What are decibels
In looking at all these definitions clearly the concept of the decibel is
very important. For any not familiar with this unit, I think the following
two links are very helpful in becoming acquainted with how decibels work and
why they are so common. The primary need is in dealing with exponential
phenomena. Intervals, differences or ranges are always ratios and decibels
always take the log of the ratio to make a linear representation of those
intervals, differences or range. In fact using decibels to measure Dynamic
Range implicitly shows that Dynamic Range must be a range from minimum to
maximum signal.
------------------- Summary
In this post I have concentrated on dynamic range as it applies to
audio signals. However, the concept of dynamic range may be applied
to many fields. In all of them, Dynamic Range is a range of values where
the system is working as advertized. The range is specified by a
maximum and a minimum value. All values within the range are possible
as far as the real world is concerned i.e. the range is a continuous
range. Digital systems are used just about everywhere now and the
digitization may quantize values within a dynamic range. This may
make it appear that there are discrete, distinguishable values
within a range, but this is purely an artifact of the digital
implementation and digital representation of the data. It is no way
changes the basic concept of dynamic range -- there are no discrete
levels, and there is no notion of dynamic range being a "number of
levels".
-----
I guess I've said enough now. I've spent a fair amount of time to insure
the accuracy of what I've written. I'd be glad to discuss or clarify or
expound on any of it as well.
Thanks,
Roy
Roy Harrington
roy@harrington.com
Black & White Photography Gallery
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