Estimation of amplitude and standard deviation of noisy sinusoidal signals
What's it about?
Accurate estimation of the amplitude of a sinusoidal signal can be obtained if the phase is properly modeled or known. Otherwise, the amplitude is biased because of the noise. We show for the first time that the amplitude and standard deviation of a noisy sinusoid can be accurately estimated without any particular form of the phase.
Why is it important?
Conventional sine-fitting algorithms consider sinusoidal signals with well-defined phases (e.g., linear phase functions). On the other hand, our method works with sinusoids whose phase can be nonlinear, discontinuous, and unknown.
This work offers a new approach for sinusoidal signal processing. Since the encoded phase is not a hard restriction (the phase can even be unknown), potential applications such as automatic tuning of blind methods for noise filtering and gamma calibration of digital fringe projection systems are possible.