# Digital Communications : Distortion signal

1. Jul 18, 2011

### naspek

hey there.. i just don't know how to start answering this question..
please help me get through this question.. thanks..

A channel has amplitude response and phase shift shown in the link below. State what type of distortion is imposed for each of the inputs given below:
i) (cos 20 pi t) + (2 cos 140 pi t)
ii) (cos 130 pi t) + (6 cos 180 pi t)

http://imageshack.us/photo/my-images/847/66626643.jpg/

[PLAIN]http://img847.imageshack.us/img847/9726/66626643.th.jpg [Broken]

Last edited by a moderator: May 5, 2017
2. Jul 18, 2011

### Ecthelion

Well, how would you define amplitude and phase distortion? What are the frequencies that each of the two signals you listed carry? Notice your graphs have an x-axis of "frequency."

When you look at the particular frequencies that your input signal has on the graphs of the channel, what are these plots doing to your input?

Try starting with those questions and see what you come up with. Lining up the amplitude and phase plots (one on top of the other) may help your interpretation.

3. Sep 23, 2011

### 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?

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