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?
What is the optimal estimator?
Started by ●December 3, 2011
Reply by ●December 3, 20112011-12-03
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
Reply by ●December 3, 20112011-12-03
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
Reply by ●December 3, 20112011-12-03
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
Reply by ●December 3, 20112011-12-03
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 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.And we *can* tell the difference, if you try and disguise a homework assignment as real work. Rune
Reply by ●December 3, 20112011-12-03
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. �����������������������������������������������������������������������
Reply by ●December 4, 20112011-12-04
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 rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●December 4, 20112011-12-04
On Dec 4, 2:41�am, 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 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?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
Reply by ●December 4, 20112011-12-04
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. > > RuneThink 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?
Reply by ●December 4, 20112011-12-04
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
