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Consider an unknown DC level in a white Gaussian noise with zero mean
and unknown variance. The value of the DC level is restricted to a
range of [A0, A1], the observations, that is the DC level plus WGN are
also restricted in this range. Then what is the optimal estimator for
the DC level and the variance of the noise?

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On 3 Des, 14:41, zqchen <zhiqun.c...@gmail.com> wrote:
> Consider an unknown DC level in a white Gaussian noise with zero mean
> and unknown variance. The value of the DC level is restricted to a
> range of [A0, A1], the observations, that is the DC level plus WGN are
> also restricted in this range. Then what is the optimal estimator for
> the DC level and the variance of the noise?

Homework?

If not, check out vol. I of van Trees.

Rune

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On Sat, 03 Dec 2011 05:41:48 -0800, zqchen wrote:

> Consider an unknown DC level in a white Gaussian noise with zero mean
> and unknown variance. The value of the DC level is restricted to a range
> of [A0, A1], the observations, that is the DC level plus WGN are also
> restricted in this range. Then what is the optimal estimator for the DC
> level and the variance of the noise?

Nonlinear.

Tell us more.  If it's a real application tell us what it is.  If it's 
homework, tell us that, or go talk to your TA.

We _will_ help you with homework -- we'll just help you differently than 
we would if it were real work.

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

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On Sat, 03 Dec 2011 11:04:35 -0600, Tim Wescott wrote:

> On Sat, 03 Dec 2011 05:41:48 -0800, zqchen wrote:
> 
>> Consider an unknown DC level in a white Gaussian noise with zero mean
>> and unknown variance. The value of the DC level is restricted to a
>> range of [A0, A1], the observations, that is the DC level plus WGN are
>> also restricted in this range. Then what is the optimal estimator for
>> the DC level and the variance of the noise?
> 
> Nonlinear.
> 
> Tell us more.  If it's a real application tell us what it is.  If it's
> homework, tell us that, or go talk to your TA.
> 
> We _will_ help you with homework -- we'll just help you differently than
> we would if it were real work.

Optimal in what sense?  Maximum likelihood?  MMSE?  Some other cost 
function?

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

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On 3 Des, 18:04, Tim Wescott <t...@seemywebsite.com> wrote:
> On Sat, 03 Dec 2011 05:41:48 -0800, zqchen wrote:
> > Consider an unknown DC level in a white Gaussian noise with zero mean
> > and unknown variance. The value of the DC level is restricted to a rang=
e
> > of [A0, A1], the observations, that is the DC level plus WGN are also
> > restricted in this range. Then what is the optimal estimator for the DC
> > level and the variance of the noise?
>
> Nonlinear.
>
> Tell us more. =A0If it's a real application tell us what it is. =A0If it'=
s
> homework, tell us that, or go talk to your TA.
>
> We _will_ help you with homework -- we'll just help you differently than
> we would if it were real work.

And we *can* tell the difference, if you try and
disguise a homework assignment as real work.

Rune

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On 12/3/2011 8:41 AM, zqchen wrote:
> Consider an unknown DC level in a white Gaussian noise with zero mean
> and unknown variance. The value of the DC level is restricted to a
> range of [A0, A1], the observations, that is the DC level plus WGN are
> also restricted in this range. Then what is the optimal estimator for
> the DC level and the variance of the noise?

My earlier post got lost. I'll ask again.

Doesn't zero mean imply that the DC level is zero?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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On 12/3/11 10:34 PM, Jerry Avins wrote:
> On 12/3/2011 8:41 AM, zqchen wrote:
>> Consider an unknown DC level in a white Gaussian noise with zero mean
>> and unknown variance. The value of the DC level is restricted to a
>> range of [A0, A1], the observations, that is the DC level plus WGN are
>> also restricted in this range. Then what is the optimal estimator for
>> the DC level and the variance of the noise?
>
> My earlier post got lost. I'll ask again.
>
> Doesn't zero mean imply that the DC level is zero?

i think that the additive error signal has no DC in it (because if it 
*did* have DC, that would simply blend into the DC level the OP wants to 
measure).

my question is why isn't a simple average or LPF (with DC gain of 0 dB) 
the optimal estimator?

-- 

r b-j                  r...@audioimagination.com

"Imagination is more important than knowledge."

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On Dec 4, 2:41=A0am, zqchen <zhiqun.c...@gmail.com> wrote:
> Consider an unknown DC level in a white Gaussian noise with zero mean
> and unknown variance. The value of the DC level is restricted to arange o=
f [A0, A1], the observations, that is the DC level plus WGN are
> also restricted in this range. Then what is the optimal estimator for
> the DC level and the variance of the noise?

Just integrate it ie a low pass filter. (since a pure integrator would
drift off to infinity due to the dc level). Can't see how you would
get better than that.

Hardy

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On 12=D4=C24=C8=D5, =C9=CF=CE=E71=CA=B123=B7=D6, Rune Allnor <all...@tele.n=
tnu.no> wrote:
> On 3 Des, 18:04, Tim Wescott <t...@seemywebsite.com> wrote:
>
> > On Sat, 03 Dec 2011 05:41:48 -0800, zqchen wrote:
> > > Consider an unknown DC level in a white Gaussian noise with zero mean
> > > and unknown variance. The value of the DC level is restricted to a ra=
nge
> > > of [A0, A1], the observations, that is the DC level plus WGN are also
> > > restricted in this range. Then what is the optimal estimator for the =
DC
> > > level and the variance of the noise?
>
> > Nonlinear.
>
> > Tell us more.  If it's a real application tell us what it is.  If it's
> > homework, tell us that, or go talk to your TA.
>
> > We _will_ help you with homework -- we'll just help you differently tha=
n
> > we would if it were real work.
>
> And we *can* tell the difference, if you try and
> disguise a homework assignment as real work.
>
> Rune

Think about a pixel with unknown grayscale value corrupted by WGN. The
grayscale value and the observation are all restricted in the range of
0 to 255. If the value and noise variance are to be estimated, what
are the best estimator?

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On Sat, 03 Dec 2011 22:34:14 -0500, Jerry Avins wrote:

> On 12/3/2011 8:41 AM, zqchen wrote:
>> Consider an unknown DC level in a white Gaussian noise with zero mean
>> and unknown variance. The value of the DC level is restricted to a
>> range of [A0, A1], the observations, that is the DC level plus WGN are
>> also restricted in this range. Then what is the optimal estimator for
>> the DC level and the variance of the noise?
> 
> My earlier post got lost. I'll ask again.
> 
> Doesn't zero mean imply that the DC level is zero?
> 

I hope that he means the Gaussian noise is zero mean -- otherwise the 
question doesn't make much sense.

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

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