# Tracking a sine wave with noise

This will probably be an extremely simple question for some one with any background in signal processing(not my background)

Let say I have signal $$x(t)=A\sin(\omega t)$$ where A is known and $$\omega$$ is unknown. Let say I only observe a noisy signal of $$x(t)$$ at discrete time periods $$t=1,2,3....$$. My signal $$y(n)$$ has the following form $$y(n)=x(n)+\epsilon$$ where $$\epsilon\sim N(0,\sigma^2)$$. My question is , what would be the best estimate of $$y(n+1)$$ given the observations till time time period $$n$$.

• Assuming you have n evenly spaced samples of the noisy sine wave, why not curve fit a sine wave to the samples and then evaluate that fitted sine wave as desired? – Ed V Sep 21 '19 at 22:04
• tracking in this context typically means that the frequency varies over time. does your sine frequency shift with time? – user28715 Sep 22 '19 at 1:47
• Hello, fortunately, the frequency does not vary with time?Also, can you guide me resources to read about curve fitting a sine wave? – kangkan Dc Sep 22 '19 at 12:00
• @kangkanDc too bad your frequency is fixed. There is a lot of material on using an extended Kalman filter for the slowly varying frequency problem. The EKF includes a prediction step. why do you need to predict the future sample? – user28715 Sep 22 '19 at 14:54
• Imagine that one has an asset whose value varies periodically with fixed frequency(our x_t). Suppose one has a stock whose price depends noisily on the value of the asset (our y_t). In this situation, one would want to have the best prediction of y_t – kangkan Dc Sep 23 '19 at 8:49