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

[Achilleas Anastasopoulos]

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)
and if you assume Gaussian noise n(t), then
if your observation is t in (0,T)
the (maximum likelihood) estimate should minimize
the squared Euclidean distance
int_0^T |r(t)-s(t)|^2 dt
or in discrete time (with appropriate sampling Ts)
sum_k |r(k Ts)-s(k Ts)|^2

There are several simplifications (eg, if you know
apriori that the 2 amplitudes are the same, or if you know one
of t1 or t2, etc) you can try (depending on the required accuracy) but 
this is the safest way to approach the problem.

Achilleas