Calculation of snr

[A complimentary Cc of this posting was sent to
John O'Flaherty
], who wrote in article :
I think you are conflating the power in light intensity
(I=Power/Asurf) with signal power. Once the intensity is mapped into a
signal, signal power has its usual meaning. You can create signals of,
for examples, stock prices or annual rainfall, and can investigate the
power spectra of the resulting signals, without a power interpretation
for the original data. And once you have a voltage signal, it doesn't
matter what it originally represented, its power is proportional to
voltage squared, referred to a standard 1 ohm impedance.

I'm afraid you use terminology outside of their usual bounds. There
is no such thing as "signal power", "power of a voltage signal" etc.

dB = 10 * log ( Signal_voltage ^ 2 / Noise_voltage ^ 2 )
dB = 2 * 10 * log ( Signal_voltage / Noise_voltage )

These squares/twos are as much misplaced/wrong as "S" in "RMS power".

The squares, when applied to statistical analysis of signals, are
correct.

There is no "correct" thing in statistics. For example, let me
restate what you say in more "truthful" form:

The math of the L2-norm is much less tricky than math of other norms
(in spaces of functions), since it is a Hilbert norm (as opposed to
more general Banach norms). Therefore, when taught to beginners,
L2-norms are prefered as the first topic to expose.

Some people are exposed only to the 101-part of the topic, so may
think that it is all there is...

In reality, the norm to use is dictated by the "physical meaning" of
the function. E.g., in context of the signal of a photo-sensor, the
meaningful norm is the L1-norm, since each measurement already
represents energy.

For example, in a textbook*, the definition of rms SNR for a
decompressed image vs. an original image is given as the square root
of the _square_ of the row-column double sum of the pixel errors,
divided by the number of pixels.

As you can guess, the extremely low quality of US textbooks is a
recurring topic at some dinner tables... :-(

Hope this helps,
Ilya

On Wed, 28 May 2008 22:23:44 +0000 (UTC), Ilya Zakharevich wrote:

As you can guess, the extremely low quality of US textbooks is a
recurring topic at some dinner tables... :-(

I'm sure that someone here will try to make you eat our words!

In article , Floyd L. Davidson
writes
Kennedy McEwen wrote:
In article , Floyd L. Davidson
writes
Kennedy McEwen wrote:
In article , Floyd L. Davidson
writes

You were referring to the design of a system to measure
noise in the light.

No, I was explaining how to measure the signal to noise ratio that the
camera is capable of measuring.

Cameras don't measure noise ratios,

Cameras measure light, and they do so with a certain signal to noise
ratio.

Exactly.
So, in measuring light, you should have no problem with some performance
elements of a camera being defined in terms of the ratio of maximum
light power detected without saturation to minimum light power
detectable, and expressing that performance in decibels, the ratio
between the two.

The *don't* measure noise ratios.

Whatever they measure, two or more of those measurements can always be
expressed as a ratio - signal and noise being just the two examples of
relevance in this thread.

The camera is just a "black box": it takes an image in, in the form of
spatially modulated light, and produces data in a form that can be
output as an image, in the form of spatially modulated light. Nobody
cares what the SNR is at some point buried in the middle of that, they

Some photographers may not care about that SNR. The
people who design cameras do, and discerning
photographers do.

More deliberate misquoting and general dishonesty from Floyd! The whole
thread is ABOUT SNR - read the subject line! However, nobody is
interested in the SNR of some component buried in the middle of the
black box, what they are interested in is the SNR of the black box in
terms of its input and/or output. Since the output also requires
knowledge of the SNR of the display medium, in this case the output SNR
is irrelevant. Consequently the ONLY measure of relevance is input
referred, and the input to a camera is LIGHT!

care about the effect that the camera has on the image, the light, and
so it makes perfect sense to measure the performance of the camera in
terms of light power.

And that does not include measuring noise ratios of the
light.

Only you seem to think so - it is certainly relevant to know what the
ratio of maximum unsaturated light level that the camera can work with
relative to its minimum detectable light under whatever circumstances it
is operated.

In fact, for the user who is only interested in
how well a particular image is represented by a particular camera it is
probably the ONLY meaningful representation of SNR.

If someone is researching which camera to buy, they want
to know the effects that show up from different
situations. They may not label them as "SNR of the
sensor", "SNR of the read amplifier", and "SNR of the
digital output format", but that is exactly what they do
want to see comparable results for, and they do tend to
decide which model camera to purchase based on the
results they see.

Precisely, which is why the RATIO of the incident light power is the
important parameter, not the absolute light power or the SNR at some
irrelevant point in the processing chain.

"The noise in the light" is something completely different and doesn't
even need to be measured, since it is simply shot noise on the total
light amplitude.

That was my point.

No it wasn't - you think that what is being described is "the noise in
the light", however that is not the case. What is being described is
the SNR of the camera referred to its input, light. The noise in the
light is something completely different from what is being measured.

Your system to measure it is not
germane to this discussion.

Only to you.

As I mentioned in a previous post in this thread, every scanner
manufacturer who specifies the capability of their product uses the same
"input referred" definition, and users have been happily comparing
scanners for years based on such numbers and measurements from
independent 3rd parties.
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's ****ed.
Python Philosophers (replace 'nospam' with 'kennedym' when replying)

Kennedy McEwen wrote:
In article , Floyd L. Davidson
writes
The camera is just a "black box": it takes an image in, in the form of
spatially modulated light, and produces data in a form that can be
output as an image, in the form of spatially modulated light. Nobody
cares what the SNR is at some point buried in the middle of that, they

Some photographers may not care about that SNR. The
people who design cameras do, and discerning
photographers do.

More deliberate misquoting and general dishonesty from Floyd! The whole

Where is the misquote? Is that not *exactly* what you said? I
certainly didn't edit it!

The dishonesty is all on your part.

thread is ABOUT SNR - read the subject line!

So just what is your problem with discussing it honestly?

However, nobody is
interested in the SNR of some component buried in the middle of the
black box,

Well, *you* might not be! But that isn't amazing, given
what you've been saying. As I noted above, "discerning
photographers do".

what they are interested in is the SNR of the black box in
terms of its input and/or output. Since the output also requires
knowledge of the SNR of the display medium, in this case the output SNR
is irrelevant. Consequently the ONLY measure of relevance is input
referred, and the input to a camera is LIGHT!

That is absurd.

There is no point in continuing a discussion with someone
who makes statements like the above set.

--
Floyd L. Davidson http://www.apaflo.com/floyd_davidson
Ukpeagvik (Barrow, Alaska)

In article , Floyd L. Davidson
writes
Kennedy McEwen wrote:
In article , Floyd L. Davidson
writes
The camera is just a "black box": it takes an image in, in the form of
spatially modulated light, and produces data in a form that can be
output as an image, in the form of spatially modulated light. Nobody
cares what the SNR is at some point buried in the middle of that, they

Some photographers may not care about that SNR. The
people who design cameras do, and discerning
photographers do.

More deliberate misquoting and general dishonesty from Floyd! The whole

Where is the misquote?

My statement was that nobody cares what the SNR is at some point buried
in the middle of the process.

You responded with a statement about not caring about SNR - without
caveat or context, in general. In short, you misquoted and blatantly
misrepresented my statement.

Is that not *exactly* what you said? I

No I did not, and well you know it, you deceitful liar!

certainly didn't edit it!

Yes you did, in mid-sentence and deliberately to take the part you
wanted to misrepresent out of context

The dishonesty is all on your part.

Floyd, you are clearly a LIAR.

There is no point in continuing a discussion with someone
who makes statements like the above set.

Precisely.
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's ****ed.
Python Philosophers (replace 'nospam' with 'kennedym' when replying)

On Wed, 28 May 2008 22:23:44 +0000 (UTC), Ilya Zakharevich
wrote:

[A complimentary Cc of this posting was sent to
John O'Flaherty
], who wrote in article :
I think you are conflating the power in light intensity
(I=Power/Asurf) with signal power. Once the intensity is mapped into a
signal, signal power has its usual meaning. You can create signals of,
for examples, stock prices or annual rainfall, and can investigate the
power spectra of the resulting signals, without a power interpretation
for the original data. And once you have a voltage signal, it doesn't
matter what it originally represented, its power is proportional to
voltage squared, referred to a standard 1 ohm impedance.

I'm afraid you use terminology outside of their usual bounds. There
is no such thing as "signal power", "power of a voltage signal" etc.

dB = 10 * log ( Signal_voltage ^ 2 / Noise_voltage ^ 2 )
dB = 2 * 10 * log ( Signal_voltage / Noise_voltage )

These squares/twos are as much misplaced/wrong as "S" in "RMS power".

The squares, when applied to statistical analysis of signals, are
correct.

There is no "correct" thing in statistics. For example, let me
restate what you say in more "truthful" form:

The math of the L2-norm is much less tricky than math of other norms
(in spaces of functions), since it is a Hilbert norm (as opposed to
more general Banach norms). Therefore, when taught to beginners,
L2-norms are prefered as the first topic to expose.

Some people are exposed only to the 101-part of the topic, so may
think that it is all there is...

In reality, the norm to use is dictated by the "physical meaning" of
the function. E.g., in context of the signal of a photo-sensor, the
meaningful norm is the L1-norm, since each measurement already
represents energy.

For example, in a textbook*, the definition of rms SNR for a
decompressed image vs. an original image is given as the square root
of the _square_ of the row-column double sum of the pixel errors,
divided by the number of pixels.

As you can guess, the extremely low quality of US textbooks is a
recurring topic at some dinner tables... :-(

Indeed, I can imagine groups of diners, saliva and gravy dribbling
down their chins, pleasuring themselves and each other by repeatedly
raising such topics.

But enough of impertinences.

As to norms, I guess an Linfinity-norm compared to an L1-norm would
be another name for worst-case pixel deviation, and an L1-norm divided
by the total pixels would be another name for mean value. Both are
more easily calculated than RMS power.

Examples of signal power, specifically power spectrum, used outside
of the realm of electricity -
http://tinyurl.com/6467kp
http://tinyurl.com/5tm75x

Dynamic range in dB as 20log(a/b) used in calculating dynamic range of
photographic sensors (Kodak) -
http://tinyurl.com/6oec2a
which, if for no other reason, is relevant to the design of follow-on
circuitry.

SNR in dB as 20log(a/b) on the imatest site:
http://www.imatest.com/docs/noise.html

Matlab image processing toolbox using the squares of image and noise
levels for a power ratio:
http://tinyurl.com/4c2tto
and noise

A wikipedia article on SNR
http://en.wikipedia.org/wiki/Signal-to-noise_ratio
says that the SNR of an electrical signal derived from a sensor is
usually calculated by 10log, since the signal represents optical
power; however, the SNR or contrast to noise ratio is calculated as
the ratio of the mean pixel value to the standard deviation of the
pixel values. The latter is the RMS power of the deviations.

I note that the clarkvision site use absolute numbers in these
contexts.

In summary, it looks as if a link to energy in some of these sources
is respected by not squaring image values, but not in all of them.
It's a mixed picture. I haven't seen a reference, though, that
calculates noise power as a mean of absolute values of unsquared pixel
levels, or as the square root of such a mean. This is how I would
interpret your comment that the "S" in "RMS power" is misplaced. If
you have a reference to such, I would like to read it. Thank you.

--
John

[A complimentary Cc of this posting was NOT [per weedlist] sent to
David J Taylor
], who wrote in article :
dBHz is a ratio, plain and simple. You may wish to rationalise it as
"power" by saying its the power ratio in two bandwidths, if that helps
you.

Let me (somewhat) sum up the discussion, as I see it:

a) The *intent* of the unit dB is to express ratio of *intensities*
in a log-scale;

b) (According to Floyd) the NIST definition of dB contains a "misprint":
"power" is used instead of "intensity"; I would ignore the NIST
definition in what follows;

c) In several *contexts*, the square of voltage is an appropriate
metric of the intensity of an electric signal;

d) The assumption intensity ="square of voltage" is hardwired into
the definition of dBV;

e) Therefore in the contexts of (c), dBV (and differences of these,
which are plain dB's) are very appropriate measures;

f) In photosensors' signal context, intensity (of the incoming
light signal) depends linearly on voltage. In this context,
using the rule "dB are differences of dBV" leads to possibilities
of major misunderstanding.

Hope this helps,
Ilya

Ilya Zakharevich wrote:
[A complimentary Cc of this posting was NOT [per weedlist] sent to
David J Taylor
], who wrote in article :
dBHz is a ratio, plain and simple. You may wish to rationalise it as
"power" by saying its the power ratio in two bandwidths, if that helps
you.

Let me (somewhat) sum up the discussion, as I see it:

a) The *intent* of the unit dB is to express ratio of *intensities*
in a log-scale;

b) (According to Floyd) the NIST definition of dB contains a "misprint":
"power" is used instead of "intensity"; I would ignore the NIST
definition in what follows;

Except of course that is not a misprint at all, it is
the standard definition according to virtually every
standards organization. ITU, ANSI, IEEE, CCITT, my
goodness even Wikipedia agrees! But you don't...

Ignoring standard definitons to substitute your own is
quaint, but it does mean that nothing you have to say on
the topic is of any value whatever.

[valueless chatter snipped]

--
Floyd L. Davidson http://www.apaflo.com/floyd_davidson
Ukpeagvik (Barrow, Alaska)

Ilya Zakharevich wrote:
[]
Let me (somewhat) sum up the discussion, as I see it:

a) The *intent* of the unit dB is to express ratio of *intensities*
in a log-scale;

b) (According to Floyd) the NIST definition of dB contains a
"misprint": "power" is used instead of "intensity"; I would
ignore the NIST definition in what follows;

c) In several *contexts*, the square of voltage is an appropriate
metric of the intensity of an electric signal;

d) The assumption intensity ="square of voltage" is hardwired into
the definition of dBV;

e) Therefore in the contexts of (c), dBV (and differences of these,
which are plain dB's) are very appropriate measures;

f) In photosensors' signal context, intensity (of the incoming
light signal) depends linearly on voltage. In this context,
using the rule "dB are differences of dBV" leads to possibilities
of major misunderstanding.

Hope this helps,
Ilya

Yes, this is a fair summary, I think. I think we need to be very careful
about (f) though, particularly where noise is to be calculated. I would
never use dBV, for example, in that context. I see it more as a signal
level in a television context, and not for use in digital cameras.

For the light-to-voltage conversion, it seems to me that you may need to
distinguish between the "measurement" and the "power conversion" cases.
For a solar array application, it's a light power in and electrical power
out process. For the measurement application, you may be measuring
short-circuit current or open-circuit voltage, with no significant power
transfer. Do that make a difference?

Cheers,
David

[A complimentary Cc of this posting was NOT [per weedlist] sent to
David J Taylor
], who wrote in article :
c) In several *contexts*, the square of voltage is an appropriate
metric of the intensity of an electric signal;

d) The assumption intensity ="square of voltage" is hardwired into
the definition of dBV;

e) Therefore in the contexts of (c), dBV (and differences of these,
which are plain dB's) are very appropriate measures;

f) In photosensors' signal context, intensity (of the incoming
light signal) depends linearly on voltage. In this context,
using the rule "dB are differences of dBV" leads to possibilities
of major misunderstanding.

Yes, this is a fair summary, I think. I think we need to be very careful
about (f) though, particularly where noise is to be calculated. I would
never use dBV, for example, in that context. I see it more as a signal
level in a television context, and not for use in digital cameras.

I see that I did not write that (e) and (f) are mutually exclusive (I
assumed it clear, naughty me :-[ ). So (f) implies: do not use dB in
this context, unless you WANT to create a confusion (as some
manufacturers may want to...).

For the light-to-voltage conversion, it seems to me that you may need to
distinguish between the "measurement" and the "power conversion" cases.
For a solar array application, it's a light power in and electrical power
out process. For the measurement application, you may be measuring
short-circuit current or open-circuit voltage, with no significant power
transfer. Do that make a difference?

The electric model of photosensors and solar-array-cells are
absolutely different indeed. A photon hitting a photosensor DECREASES
the voltage (this adsorbs the electric energy); a photon hitting a
solar-array-cell creates the electric energy.

Still, solar-array-cells being highly non-linear, I'm not sure whether
usage of dB and dBV in their context makes any sense. People who
know, could you comment?

Thanks,
Ilya