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 a₂1 and t₀₂ > t₀₁.

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Delay Input Delay signal Output signal Σ 3.