Using the coherence function for noise reduction

With the development of hands-free radio communications there is great interest in noise cancelling or speech enhancement in a car. The authors assume that M observations are available; each one is composed of signal and noise (s _i+b _i), and s ₁ is the signal to be estimated. Whatever the distance between microphones is, the signals are strongly correlated, while the correlation between noises becomes rather weak for a sufficiently great distance. The coherence function is then a pertinent criterion to know whether a speech signal exists or not. The three methods presented use the coherence function to filter the observations so giving an estimate of the signal s ₁. The procedures presented are first shown for M=2. Then, a generalisation of these procedures is offered. The performances of the three methods have been evaluated on real noisy speech signals by objective tests (gain on the signal-to-noise ratio, distance measures) and informal listening tests.<>