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, x_k to the local telephone and route speech from the telephone to the far end. However, the hybrid is never perfect, so its output, d_k contains both the desired speech from the local telephone plus filtered speech from the far end. The adaptive filter f_k attempts to minimize the error signal ε_k by filtering the incoming far end speech into a replica, y_k 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.