Thresholded Multiple Coherence as a tool for source separation and denoising: Theory and aeroacoustic applications

Abstract The multiple coherence is a spectral analysis tool allowing the estimation of the contribution of several, possibly partially, coherent inputs to one or several outputs. This type of analysis can be conducted using a waterfall substraction approach (Conditioned Spectral Analysis framework) or using an eigenvalue analysis of the input correlation matrix (Virtual Source Analysis approaches). Those techniques are well established when dealing with converged cross-spectral estimates. In practice, this is never the case because of the finite nature of time records, and it can bring interpretation issues, particularly when increasing the number of references. The significance of the estimated coherence plays a central role in the present work. It involves the implementation of an hypothesis test based upon the statistical behavior of the estimated coherence between incoherent signals. This test, whose principle is to put to zero an estimated coherence that is below a significance threshold, is extended in this work to the multiple coherence case. The TMC (Thresholded Multiple Coherence) is first illustrated in the frame of a numerical benchmark, and then validated in a laboratory wind tunnel test where the interest for denoising purpose is demonstrated. The approach is finally applied to signals recorded inside and outside the cabin of an aircraft during a flight test. The TMC is used either from outside to inside microphones, to analyse the contribution of outside noise sources to the interior noise, or alternatively from inside to outside sensors, for flow noise rejection purpose.