English: An adaptive echo canceler for a telephone circuit. The function of H, the hybrid transformer is to route incoming speech from the far end, xk to the local telephone and route speech from the telephone to the far end. However, the hybrid is never perfect, so its output, dk contains both the desired speech from the local telephone plus filtered speech from the far end. The adaptive filter fk attempts to minimize the error signal εk by filtering the incoming far end speech into a replica, yk of the far end speech that leaks through the hybrid. Once the adaption is complete, the error signal consists entirely of speech from the local telephone.
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