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What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
Which makes it a good job interview question.
--
Rich
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
Which makes it a good job interview question.
--
Rich
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
The Widrow approximation is that quantization contributes additive noise
of 1/sqrt(12) LSB. However, the validity of that approximation requires
that the signal be at least a few LSBs in size.
However, if we assume that the approximation is valid, then for unipolar
signals the dynamic range is 7*sqrt(12), and for bipolar sinusoidal
signals it's reduced by a factor of about sqrt(8).
The exact number is
a bit arbitrary--you can argue about whether the maximum resolvable
amplitude goes out to the edges of bins 0 and 7, or the centres, or
wherever. As I said, it's on the edge of being ill-posed.
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
Which makes it a good job interview question.
How do you define dynamic range?
Ratio of max to min signal?
In which case I'll guess the min is where the lsb is kicking on 1/2 the time
and max is when 7 is kicking on 1/2 the time ...
so 6.5/.5 = 13
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
Which makes it a good job interview question.
--
Rich
On March 7, George Herold wrote:
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
Which makes it a good job interview question.
On March 5, Phil Hobbs wrote:
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
The Widrow approximation is that quantization contributes additive noise
of 1/sqrt(12) LSB. However, the validity of that approximation requires
that the signal be at least a few LSBs in size.
No, it only supposes that the signal is uniformly
distributed between quantization levels.
And it isn't the Widrow approx., it's simply an
elementary derivation of the noise power.
What's your familiarity with Widrow?
So your question is on the edge of being ill-posed.
Only in the sense that I didn't define dynamic range.
I use it in the conventional manner. Which is ....
However, if we assume that the approximation is valid, then for unipolar
signals the dynamic range is 7*sqrt(12), and for bipolar sinusoidal
signals it's reduced by a factor of about sqrt(8).
No reference or assumption of polarity is required.
You're going astray.
The exact number is
a bit arbitrary--you can argue about whether the maximum resolvable
amplitude goes out to the edges of bins 0 and 7, or the centres, or
wherever. As I said, it's on the edge of being ill-posed.
You're confused. Though you're on the right track,
considering noise and uncertainty, which influences
the analysis.
Very remarkable that almost no one has thought about
such a basic concept. It's a matter of defining the
terms, then straightforward reasoning. But intuitional
guessing won't do it -
On March 7, George Herold wrote:
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
Which makes it a good job interview question.
How do you define dynamic range?
Ratio of max to min signal?
bravo!
In which case I'll guess the min is where the lsb is kicking on 1/2 the time
and max is when 7 is kicking on 1/2 the time ...
so 6.5/.5 = 13
um, almost... keep trying -
I'll give a hint later, if necessary. Though it shouldn't be so -
See? It IS a good interview question!
--
Rich
What is the dynamic range of a 3-bit A/D converter?
How do you define dynamic range?
Ratio of max to min signal?
bravo!
In which case I'll guess the min is where the lsb
is kicking on 1/2 the time
and max is when 7 is kicking on 1/2 the time ...
so 6.5/.5 = 13
um, almost... keep trying -
See? It IS a good interview question!
Hmm well if Phil (and I) can't get it "right", then I'm
not sure how good it is.
On 03/09/2016 07:46 PM, Phil Hobbs wrote:
On 03/07/2016 04:39 PM, RichD wrote:
On March 5, Phil Hobbs wrote:
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
The Widrow approximation is that quantization contributes additive noise
of 1/sqrt(12) LSB. However, the validity of that approximation requires
that the signal be at least a few LSBs in size.
No, it only supposes that the signal is uniformly
distributed between quantization levels.
And it isn't the Widrow approx., it's simply an
elementary derivation of the noise power.
What's your familiarity with Widrow?
I took his DSP class at Stanford in about 1986. I'm repeating what he
said about it. There's nothing elementary about it whatsoever.
To expand on this a bit: it's elementary that the RMS error of a
many-bit quantization is LSB/sqrt(12).
Widrow's theorem showing that under certain assumptions (mostly that the
signal is at least several LSBs in size), quantization, which is
nonlinear, can nevertheless be modelled accurately as a linear operation
with additive noise of LSB/sqrt(12). That was widely doubted at the
time, and so became Widrow's most famous contribution. Without it,
linear systems theory would be much less useful.
Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics
160 North State Road #203
Briarcliff Manor NY 10510
hobbs at electrooptical dot net
http://electrooptical.net
Well forget about me, but if you are hiring someone to doOn March 10, George Herold wrote:
What is the dynamic range of a 3-bit A/D converter?
How do you define dynamic range?
Ratio of max to min signal?
bravo!
I should add, apparently this definition is
less well known, or accepted, than I assumed.
In which case I'll guess the min is where the lsb
is kicking on 1/2 the time
and max is when 7 is kicking on 1/2 the time ...
so 6.5/.5 = 13
um, almost... keep trying -
See? It IS a good interview question!
Hmm well if Phil (and I) can't get it "right", then I'm
not sure how good it is.
That clearly validates it.
What's your answer?
Where did your 6.5 come from?
Like the teacher said: show your work -
--
Rich
On Thursday, March 10, 2016 at 11:59:00 AM UTC-5, Phil Hobbs wrote:
On 03/09/2016 07:46 PM, Phil Hobbs wrote:
On 03/07/2016 04:39 PM, RichD wrote:
On March 5, Phil Hobbs wrote:
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
The Widrow approximation is that quantization contributes additive noise
of 1/sqrt(12) LSB. However, the validity of that approximation requires
that the signal be at least a few LSBs in size.
No, it only supposes that the signal is uniformly
distributed between quantization levels.
And it isn't the Widrow approx., it's simply an
elementary derivation of the noise power.
What's your familiarity with Widrow?
I took his DSP class at Stanford in about 1986. I'm repeating what he
said about it. There's nothing elementary about it whatsoever.
To expand on this a bit: it's elementary that the RMS error of a
many-bit quantization is LSB/sqrt(12).
OK (I'll play) do you have a reference I can look up for that?
My simple minded approach is LSB/2. Does the sqrt(12) need to assume
some noise on the signal? (And then model the noise.)
And what's up with the distinction between bipolar and unipolar?
Do I need to assume noise on both lines with bipolar?
George H.
What's _not_ elementary is
Widrow's theorem showing that under certain assumptions (mostly that the
signal is at least several LSBs in size), quantization, which is
nonlinear, can nevertheless be modelled accurately as a linear operation
with additive noise of LSB/sqrt(12). That was widely doubted at the
time, and so became Widrow's most famous contribution. Without it,
linear systems theory would be much less useful.
Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics
160 North State Road #203
Briarcliff Manor NY 10510
hobbs at electrooptical dot net
http://electrooptical.net
On 03/07/2016 04:39 PM, RichD wrote:
On March 5, Phil Hobbs wrote:
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
The Widrow approximation is that quantization contributes additive noise
of 1/sqrt(12) LSB. However, the validity of that approximation requires
that the signal be at least a few LSBs in size.
No, it only supposes that the signal is uniformly
distributed between quantization levels.
And it isn't the Widrow approx., it's simply an
elementary derivation of the noise power.
What's your familiarity with Widrow?
I took his DSP class at Stanford in about 1986. I'm repeating what he
said about it. There's nothing elementary about it whatsoever.
On Thursday, March 10, 2016 at 11:59:00 AM UTC-5, Phil Hobbs wrote:
On 03/09/2016 07:46 PM, Phil Hobbs wrote:
On 03/07/2016 04:39 PM, RichD wrote:
On March 5, Phil Hobbs wrote:
What is the dynamic range of a 3-bit A/D converter?
I predict no one will get this.
The Widrow approximation is that quantization contributes additive noise
of 1/sqrt(12) LSB. However, the validity of that approximation requires
that the signal be at least a few LSBs in size.
No, it only supposes that the signal is uniformly
distributed between quantization levels.
And it isn't the Widrow approx., it's simply an
elementary derivation of the noise power.
What's your familiarity with Widrow?
I took his DSP class at Stanford in about 1986. I'm repeating what he
said about it. There's nothing elementary about it whatsoever.
To expand on this a bit: it's elementary that the RMS error of a
many-bit quantization is LSB/sqrt(12).
OK (I'll play) do you have a reference I can look up for that?
My simple minded approach is LSB/2. Does the sqrt(12) need to assume
some noise on the signal? (And then model the noise.)
And what's up with the distinction between bipolar and unipolar?
Do I need to assume noise on both lines with bipolar?