Auto-correlation function estimation considering noise reduction

In traditional signal analysis, signal power and signal-to-noise ratio are estimated using the signal's stochastic properties. Those are related to a signal's auto-correlation function (ACF). Assuming that signal and noise are uncorrelated wide-sense stationary stochastic processes, the signal power can be obtained by subtracting the noise power from the signal's power in noise. This demands auxiliary data exclusively consisting of noise.

However, there are situations where signal areas that only contain noise are difficult to identify or only little data is available. In such cases, considerable losses in accuracy may have to be accepted when estimating the signal power.

The method introduced here promises to significantly reduce the influence of noise in ACF estimation without the need for auxiliary noise data. The technique involves replacing the ACF magnitudes around the Center-lag area with a regression polynomial. In its initial design, the method applies to damped, sinusoidal signals.

The numerical study presented below yields promising results. It demonstrates that the method can provide reliable signal power estimates for typical applications, making it a practical and valuable tool.