# Reconstructing sine wave from samples

Suppose there is a sine wave signal, like the following:

$$V(t) = M * sin(\phi_0 + \omega*\Delta t)$$

I can have it sampled and obtain $V_1$, $V_2$ and $V_3$ at $t_1$, $t_2$ and $t_3$ such that $t_1..t_3$ is within one half-wave which would give a system of three equations with three things to find and no ambiguity.

Is it possible to solve this for $M$, $\phi_0$ and $\omega$? If that's impossible, what is the next best thing?

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This will form a nonlinear system of three equations and three unknowns and as such will likely require a numerical solution. –  kyp4 Nov 27 '13 at 12:44
Since it's nonlinear, you'll have to do something more than the usual Ax=b estimation. I'd suggest you define a cost function that is the sum of squared differences and than solve it with a simplex-style search. If you are using matlab, look at fminsearch. –  AnonSubmitter85 Dec 5 '13 at 2:29