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.

H-Bonds in Crambin: Coherence in an α-Helix

“…Other methods may improve on classical engineering approaches, but it is unrealistic to expect them to be available, validated, and documented for some time. In fact, most recent reviews use classical methods in single input–output systems like ours. , Relevant promising approaches in two (and three) dimensions are described in refs. ,,,,, ,,,,, …”

“… 10 , 13 Relevant promising approaches in two (and three) dimensions are described in refs. 8 , 11 , 12 , 32 , 45 , 50 8 , 11 , 12 , 32 , 45 , 50 …”

“…10,13 Relevant promising approaches in two (and three) dimensions are described in refs. 8,11,12,32,45,508,11,12,32,45,50 While not too common in classical MD, there actually is a long history of using the frequency response function H(f) in materials science and biochemistry. Measurements of H( f) have been the basis of much of material science for more than a century, 17,51 as has been carefully explained.…”

“…Use of the coherence function is well established in engineering. Estimators of coherence are described in classic literature , and are used with little change in modern literature. − One of us (Eisenberg) has used these methods in physiology to analyze the electrical structure of cells and tissues, , as has been reviewed. − …”