Some Considerations on the Application of the Volterra Representation or Nonlinear Networks to Adaptive Echo Cancellers

representation of nonlinear systems generalized adaptive echo canceller We prove that the proposed zero and finally we suggest The Volterra functional representation of a nonlinear system is a generalization of the well known convolution integral used for linear systems. The v a l i d i t y conditions for the Volterra model are sufficiently w e a k to be satisfied in m a n y practical applications. In this paper we apply the Volterra representation to the echo control problem and propose a generalized adaptive echo canceller which compensates for nonlinear echo paths. We prove that the proposed echo canceller converges and reduces the echo to zero in the absence of noise. We also suggest other applications for the adaptive echo canceller presented. II. T H E VOLTERRA FUNCTIONAL REPRESENTATION OF A NONLINEAR 2-PORT For linear systems it is well known that the impulse response completely determines the input-output relationship. The output signal, y ( t ) , is functionally related to the input, x(t), by the convolution integral, (1) where h{t) is the system impulse response. It has been demonstrated by other investigators 1 - 3 that nonlinear systems, whose outputs do 2797