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i had this doubt previously queried in another forum, but unfortunately had no answer.

Consider a signal 3^n u[n]. Take its Z transform, which is Z/(Z-3). Now i know that in real sense, Z is a delay operator. We can model a system such that Z/(Z-3) is an operator and 3^n is its output, when given a particular input x(n). You mention the ROC of the system to be |Z|>3, which is understandable in mathematical sense, because we form a binomial expression in Z , and for that expression to be valid, it must converge thus subsequently yielding |Z|>3 as the condition for that expression to make sense.

BUT! Here comes the exciting part of my doubt

does |Z|>3 makes physical sense???????

i know Z is an operator. How can an operator be a number as dictatated by ROC???? From what i know operators act on numbers. Operators are not numbers themselves. Operators are independent of numbers

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  • $\begingroup$ is it $3^n$? or is it $3^n u[n]$ or $3^n u[-n]$? (where $u[n]$ is the unit step function.) $\endgroup$ Aug 18, 2021 at 4:32
  • $\begingroup$ oh sorry , the function is right sided i.e 3^n u[n] $\endgroup$ Aug 18, 2021 at 4:40

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does |Z|>3 makes physical sense???????

Why would it have to ? Math is math and not concerned about physicality. When you are using math, you need to decide whether you are using the math in the right context or not.

Stupid example: math gives you a plastic bowl: you can make batter in it (good), you can shove in the microwave (ok, but not yummy), and can also put it the oven (bad, it melts). What you do with it doesn't change the basic nature of the plastic bowl, it is what it is and it's up to you to decide what to do with it (or not) in the context of your specific application.

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  • $\begingroup$ Yeah, i agree. If the ROC has no physical sense and is just a mathematical tool , then why do they mind to analyze it? $\endgroup$ Aug 19, 2021 at 3:56
  • $\begingroup$ Because all physical models are based on assumptions that limits their applicability and you need to understand where these limits are. If you are interested in what happens on the unit circle in the z-plane than you need to make sure that the ROC of all z-transforms you are using includes the unit circle. $\endgroup$
    – Hilmar
    Aug 19, 2021 at 20:39
  • $\begingroup$ Thanks for the insight! $\endgroup$ Aug 21, 2021 at 12:04

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