Hi! Explain please, whence follows that the statistics of the second order does not contain the phase information, and statistics of the high order comprise the phase information. It would be desirable to understand physics of the given phenomenon. Thanks.
high order statistics
Started by ●October 30, 2007
Reply by ●October 31, 20072007-10-31
x .* conj(x) is even and zaps the phase. But for odd powers there can't be as many conj(x) as there are xes, so the phase remains. Is that what you're after? -mn
Reply by ●November 1, 20072007-11-01
On 30 Okt, 12:10, "alex65111" <alex65...@list.ru> wrote:> Hi! > > Explain please, whence follows that the statistics of the second order > does not contain the phase information, and statistics of the high order > comprise the phase information.No phase survives the operation z*conj(z) for complex-valued z.> It would be desirable to understand > physics of the given phenomenon.There is no physics involved, only maths. Rune
Reply by ●November 1, 20072007-11-01
Thanks for answers, but questions still is. 1 question. When we find the statistical moments for real numbers, we simply multiply X on X. And when X is complex, we necessarily take conj. Why complex numbers cannot be multiplied without conj? Would multiply complex h on complex h without conj and would not lose a phase? 2 question. In many publications it is written, that the moments above the second keep the phase information (without a difference - the even or odd moment). How it is evidently possible to show, what the fourth moment keeps a phase?
Reply by ●November 1, 20072007-11-01
Rune Allnor wrote: ...> There is no physics involved, only maths.I don't see how that might be valid for anything that relates to the real world. Sometimes the relation is obscure, but even then, it usually has value when uncovered. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 1, 20072007-11-01
On 1 Nov, 16:19, Jerry Avins <j...@ieee.org> wrote:> Rune Allnor wrote: > > ... > > > There is no physics involved, only maths. > > I don't see how that might be valid for anything that relates to the > real world.The question was about higher order statistics. No physics there. Statistics might be useful when working with physics, but the converse is not true. Rune
Reply by ●November 1, 20072007-11-01
>>Statistics might be useful when working with physics, but the converse isnot true On that I respectfully disagree. To quote Richard Owlett (from http://www.dsprelated.com/showmessage/83474/1.php) "College physics led to understanding previous semester's calculus, not vice versa as intended." This can be so true... -mn
Reply by ●November 1, 20072007-11-01
Rune Allnor wrote:> On 1 Nov, 16:19, Jerry Avins <j...@ieee.org> wrote: >> Rune Allnor wrote: >> >> ... >> >>> There is no physics involved, only maths. >> I don't see how that might be valid for anything that relates to the >> real world. > > The question was about higher order statistics. No physics > there. Statistics might be useful when working with physics, > but the converse is not true.The question was why phase information isn't carried across to second-order statistics. I bet there's a physical explanation even it I can't see it off hand. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 1, 20072007-11-01
On 1 Nov, 20:43, Jerry Avins <j...@ieee.org> wrote:> Rune Allnor wrote: > > On 1 Nov, 16:19, Jerry Avins <j...@ieee.org> wrote: > >> Rune Allnor wrote: > > >> ... > > >>> There is no physics involved, only maths. > >> I don't see how that might be valid for anything that relates to the > >> real world. > > > The question was about higher order statistics. No physics > > there. Statistics might be useful when working with physics, > > but the converse is not true. > > The question was why phase information isn't carried across to > second-order statistics. I bet there's a physical explanation even it I > can't see it off hand.Why waste a lot of time and effort in a search for a non-existent physical explanation when the maths is straightforward? Rune
Reply by ●November 1, 20072007-11-01
On 1 Nov, 18:54, "mnentwig" <mnent...@elisanet.fi> wrote:> >>Statistics might be useful when working with physics, but the converse is > > not true > > On that I respectfully disagree. > To quote Richard Owlett (fromhttp://www.dsprelated.com/showmessage/83474/1.php) > > "College physics led to understanding previous semester's calculus, not > vice versa as intended." > > This can be so true..."Can" being the operative word. The key to obtain insight is to see when the simplifying analogies no longer hold, and in fact obfuscate more than they help. Rune
