An input signal x(t) is sent through three different communication channels, and the corresponding output signals are found to have the following expressions: y(t) = x(t) + 0.2x(t 3) z(t) = x(t/2) w(t) = x(t) For each of these channels, verify mathematically if the channel is linear time-invariant (LTI), and in that case write an expression of the channel impulse response h(t) and transfer function H(f), also known as frequency response.