In this problem we use the LMS algorithm to formulate an adaptive echo canceller for use in a digital subscriber line. The basic principle of adaptive echo cancellation is to synthesize a replica of the echo and subtract it from the returned signal in an adaptive manner, as illustrated in Figure. The synthesized echo, denoted by r [n], is generated by passing the transmitted signal through an adaptive filter that ideally matches the transfer function of the echo path. The returned signal, consisting of the sum of actual echo r[n] and the received signal xml, may be viewed as the desired response for the adaptive filtering process. Using the LMS algorithm, formulate the equations that define the operation of adaptive echo canceller in Figure.

Received signal, z(nl Adapive filter Hybrid ) eln) xla) + r[n]