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# linear system with a zero in the transfer function

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#### sharas

##### Member level 4
Hi,

If I have a linear system with a zero in it's tranfer function. This mean that the phase of the output will precede the phase of the input.

How is this possible ??

Thanks,

Sharas

Hi sharas,
do you realize that a positive phase shift of - let´s say - +90 deg is equivalent to a negative shift of -270 deg ?

### sharas

Points: 2
Hi Sharas

That means that if you put a pure sinusoidal signal of some frequency at the input, the output is a sinusoid of the same frequency, with some aplitude and whose phase advances the output. Pure sinusoidal means that it does not have a start, it comes from t=-infinity.
It you start to apply the sinusoid at some time, the ouput has a transient and after some time (when the transient has extinguished enough) you see the steady state: the output phase "advances" the input.
There is no violation of causality. The output "advances" bacause of all the history. If the input has a change (for example, if it stops or abruptly changes its phase, its ampltude or its frequency) that is not forecasted in advance at the output. That produces another transient, after which the ouput reaches the new staedy state.
I hope this helps you

Regards

Z

### sharas

Points: 2
Thanks guys for the replies.

I understand Zorro's reply: That means that for a pure sinus casuality is indeed vilolated?

LvW, can you please elaborate hoe this solves casuality in the time domain for an idiot as myself?

Thanks,

sharas

sharas said:
That means that for a pure sinus casuality is indeed vilolated?

No. Causality is not violated. I tried to show that by examples. The output does not precede the output. In the case of a pure sinusoid (steady state), simply at some time the output has the same shape that will have the output some time later.
Regards

Z

### sharas

Points: 2
sharas said:
That means that for a pure sinus casuality is indeed vilolated?

Causality is irrelevant for a pure sinus since the signal itself is not causal. It has no "beginning" in a temporal meaning, and no "end".

Points: 2