Noise reduction with sinusoidal signals

Three methods using higher order statistics (HOS) are proposed to solve a particular noise cancelling application: the elimination of rotating machines noises. In this case, the signal and noise reference both contain sinusoidal components of the same frequency and random parts. The inputs are necessary uncorrelated. These methods are developed in the frequency-domain with the help of first, second and third order moments of the observations. The authors first propose a probabilistic approach in order to identify the complex gain of a linear filter between reference and the additive noise. The step to the deterministic approach may be only realized under some conditions on the estimation window of first, second and third order moments. Then they compare these practical methods; they compute their quadratic error using limited temporal windows. They show that the method taking into account third order information is particularly attractive for low signal to noise ratio in the noise reference; it has a lower quadratic error than more classical methods using only second order information.