Removal of partially correlated noise to improve signal to noise ratio - a theoretical study

Time correlation and decorrelation are well established tools to improve the signal to noise ratio of a system, yet they are often poorly understood. When several unwanted signals are correlated they are much easier to remove from uncorrelated wanted signals than vice versa, where a much poorer improvement is possible. A case in point is the removal of wind noise from microphone signals. The situation is further compounded when one or other of the signals is only partially correlated, or different spectral content is differently correlated. This paper looks at the theoretical improvement in signal to noise ratio when either the signal or the noise are correlated to different degrees. Application to real microphone signals and noise is discussed