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# Digital Communications System : Ideal Communication System

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#### naspek

##### Member level 1
A signal x(t) is transmitted over a channel and appears at the channel output as y(t) = 2x(t - 3).
Find out whether it is a distortionless transmission or not.

how am i going to start answering this question?

First of all you should recall conditions for distortionless transmission. You can consider two approaches to this problem:
a) in time domain
Transmission of x(t) signal is distortionless if the output signal y(t) is defined by:
y(t) = Cx(t - to)

b) in frequency domain
For transmission through the system without distortion the frequency response of the system must satisfy two conditions:
|H(jw)| = C, and arg{H(jw)} = -wto
where:
w = omega

Now I think You are able to give answer for your question by yourself.

PS. If You want to know a little more You can study chapter 8.2 Haykin's "Signals and Systems" book.

It is distortion less for sure, all you did is multiplying by a constant and delaying which corresponds to a constant gain transfer function with a linear phase.

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