so i have asked my very first question on the dsp stack exchange site...

On 9/24/2014 9:34 PM, robert bristow-johnson wrote:
>
> i have to confess, Bob, that i am not persuaded.  i set up the question
> a bit more with the start of an answer (in two modes, one using the
> language of Hilbert Spaces and the other not).  please take another look
> at the page, if you want.
>
> L8r,
>

Hi,

To borrow a quote from "Monday Starts on Saturday", "It's nonsense to 
look for a solution if it already exists. We are talking about how to 
deal with a problem that has no solution."

The problem is that your problem in the general form as expressed in 
your initial post has no solution which is proved by a few 
counterexamples provided here.

May be, it's prudent to provide some additional constraints. For 
example, simulations I've run indicate that your theorem seem to work IF 
the signals X, Y and Z are both even AND convex curves (within a 
period). It doesn't work if X,Y, and Z are only even but not convex. It 
doesn't work if X,Y, and Z are only convex but not even.

Hope that helps.

Evgeny.

Robert

I've only spent a few minutes thinking about this so I'm likely not correct. I have one question though. The cross- correlation between any 2 of your 3 periodic signals could have a negative peak instead of a positive peak. In that case your formula for finding the location of the max Rxy would fail ( well your formula will give some answer but should you be looking for the location of the max abs(Rxy)  instead ?)

Bob

On 9/25/2014 2:31 PM, Evgeny Filatov wrote:
> On 9/24/2014 9:34 PM, robert bristow-johnson wrote:
>>
>> i have to confess, Bob, that i am not persuaded.  i set up the question
>> a bit more with the start of an answer (in two modes, one using the
>> language of Hilbert Spaces and the other not).  please take another look
>> at the page, if you want.
>>
>> L8r,
>>
>
> Hi,
>
> To borrow a quote from "Monday Starts on Saturday", "It's nonsense to
> look for a solution if it already exists. We are talking about how to
> deal with a problem that has no solution."
>
> The problem is that your problem in the general form as expressed in
> your initial post has no solution which is proved by a few
> counterexamples provided here.
>
> May be, it's prudent to provide some additional constraints. For
> example, simulations I've run indicate that your theorem seem to work IF
> the signals X, Y and Z are both even AND convex curves (within a
> period). It doesn't work if X,Y, and Z are only even but not convex. It
> doesn't work if X,Y, and Z are only convex but not even.
>
> Hope that helps.
>
> Evgeny.
>

Oops. I've meant to say that a reasonable guess about the sufficient 
conditions for Robert's theorem is that the shapes of signals X, Y, and 
Z are both symmetrical and rise monotonously from their minimum to 
maximum values (within a period, that is).

Even then you would have to deal with the ambiguity related to the fact 
that there might be more than one maximum in cross-correlation functions 
per period, so that's assuming there is only one.

Evgeny.