Problem 2

If s signal, x(t), is transmitted over a channel that produces a received signal y(t) where

y(t) = 2 x(t-0.003 μs) +0.004-x(t -0.005 μs)

a) For the case of this input x(t) = x₁ (t) to the system above what would be the output of

this channel? x₁(t) → y₁ (t), Find an expression for y₁ (t).

input is x₁(t) = + 1.1-cos(2n500t)? (write an expression for output)

b) For the case of this input x(t) = x₂(t) = 8(t), an impulse, to the same system again,

what would be the response, y(t) = y₂(t), x₂ (t)→ y₂(t), Find an expression for

y₂(t).

c) Is this system LTI?

d) Does this channel/system provide distortionless transmission?

e) What would be the transfer function, H(f), for this system?