Re: [Discuss-gnuradio] Using DSP for precise zero crossing, measurement?

[Lee Patton]

On Mon, 2006-09-18 at 12:32 -0400, Achilleas Anastasopoulos wrote:
> John,
> 
> If want to measure the time difference between two sine waves in noise 
> and accuracy is your primary objective, then you should start with the
> "optimal" solution to the problem and not with an ad-hoc technique
> such as measuring the zero crossings.
> 
> In the simplest scenario, if your model looks like:
> s(t) = s(t;A1,A2,t1,t2) = A1 sin(w (t-t1)) + A2 sin(w (t-t2))
> r(t)=s(t)+n(t)

John, 

Does your model look like the one Achilleas described above, or is it
like the following? 

s1(t) = A1*sin(w1(t-t1)+phi1); r1(t) = s1(t) + n1(t)
s2(t) = A2*sin(w2(t-t2)+phi2); r2(t) = s2(t) + n2(t)

In this model, you have separate observations of each sinusoid.  i.e.,
r1(t) and r2(t) respectively. 


Bob, Achilleas -

On an intuitive level, it seems to me that (ML) estimating the
parameters of s1(t) and s2(t) from r1(t) and r2(t) respectively, instead
of jointly from r(t) = s1(t)+s2(t)+n(t), would result in better
accuracy.  Do you agree?  At the very least, I think an adaptive
technique would converge faster if only three parameters needed to be
estimated instead of six. (Obviously, you would estimate both signals in
parallel to get dphi = phi1-phi2).

-Lee