Suppose that we want to measure the temperature, X(t), in a manufacturing process. Since the measurements are corrupted by additive noise, N(t), independent of the temperature, we reconstruct the true...

Suppose that we want to measure the temperature, X(t), in a manufacturing process. Since the measurements are corrupted by additive noise, N(t), independent of the temperature, we reconstruct the true temperature with an optimal filter. Assuming
  find the covariance function of the output signal,