Some radio systems suffer from multipath distortion, which is caused by the existence of more than one propagation path between the transmitter and the receiver. Consider a channel the output of which, in response to a signal s (t), is defined by (in the absence of noise) x (t) = a1s (t — t01) + a2s (t — t02) where a1 and a2 are constant, and t01 and t02 represent transmission delays. It is proposed to use the three-tap delay-lime-filter of Figure to equalize the multipath distortion produced by this channel.
(a) Evaluate the transfer function of the channel.
(b) Evaluate the parameters of the tapped-delay-line filter in terms of a1, a2, t01, and t02, assuming that a2 << a1 and t02 > t01.