Hello, I am confused about a system property and hope that someone canpoint me t

Question

Hello,
I am confused about a system property and hope that someone canpoint me to where I'm wrong. It's a bit long but very simple forsomeone that knows this. No calculation involved.

My confusion is between Time shifting of a signal and Causalproperty of a system.

    As I understand, If x(t) is some signal, thenx(t-to) is a shifted version of that signal. And if to>0then
x(t-to) is shifted to the right, which is the future,and so thesignal is delayed. And when to<0 then x(t-to) is shifted to theleft which is the past and so the signal is advanced.
    A system is causal if it's output depends on aninput at present or past time only.
Ok here is my confusion: A system which produces this kind ofinput x(t) to output y(t) relationship      y(t)=x(t+5) is not a causalsystem.

x(t+5)=x(t-(-5)), here to=-5 is < 0, so the signal x(t+5) is ashifted version of x(t).
x(t+5) is shifted to the left, which is the past, so thesignal is an advanced version of x(t).

I think I'm getting the past and future mixed up here.

Can someone explain why y(t)=x(t+5) is not a causal system I/Orelationship.

Explanation / Answer

The defination which you had given is correct , i think u confusedbetween past and future. now let us take your ex. y(t)=x(t+5) put t =0 we get: y(0)=x(0+5) here at current instance t=0 ,output depends on future value ofinput .hence system is non causal. HOPE THIS WILL HELP YOU

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