Joint channel and echo impulse response shortening on digital subscriber lines

A new scheme for joint shortening of two long impulse responses using a single finite impulse response (FIR) equalizer is presented. The optimum settings, in the mean square error (MSE) sense, of the equalizer and the two (unit-tap constrained) shortened impulse responses are derived. The main application of interest is joint shortening of the channel and echo impulse responses for high-speed transmission on digital subscriber lines.