Amplitude and Phase Distortion Signal

[naspek]

Find the output to each of the inputs given below. For which cases is the transmission
distortionless? For the other cases, indicate what type of distorsion in imposed.
(a) cos(48πt) + 5 cos(126πt)
(b) cos(126πt) + 0.5 cos(170πt)
(c) cos(126πt) + 3 cos(144πt)
(d) cos(10πt) + 4cos(50πt)
Solution: Note that the four input signals are of the form xi(t) = a cos(2πf1t)+b cos(2πf2t),
for i = 1, 2, 3, 4. Consequently, their Fourier transforms consist of four impulses:
Xi(f) = a/2[δ(f + f1) + δ(f − f1)] + b/2[δ(f + f2) + δ(f − f2)], i= 1, 2, 3, 4.
With this in mind, we have the following
(a) Amplitude distortion; no phase distortion.
(b) No amplitude distortion; phase distortion.
(c) No amplitude distortion; no phase distortion.
(d) No amplitude distortion; no phase distortion.

I've got the answer... as mentioned above..
However.. i just can't understand it..
should i calculate something to proof that the signal have amplitude or phase distortion?
please give me some idea to understand this question..

 

[permute]

there is more to the question. "find the outputs" is the relevant part. As given, this makes no sense -- nothing is given to put this in context.