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