Understanding Causality: Is y(n) = x(n3) a Causal System?

[caramello]

Hi,

I need help in determining if a system is causal or not. So what I knew is that for a system to be causal is that it has to depend on past and present inputs. However, I don't completely understand the meaning of that definition. So for example if I have a system y(n) = x(n³) how do we know if its input depends on its past inputs or not? i mean obviously if we put in some values of n = 2, it will definitely affect the output of n³=2³=8. So the system is then causal?

I am really confused about this. Thanks!

 

[Valkarie]

Yes, this system is causal. Causality means that the output of a system at any given time is only dependent on the present and past inputs and not on future inputs. In this particular example, the output at a given time step (n) will be determined by the input from the past three time steps (n-3, n-2, and n-1). Therefore, the system is indeed causal.

 

[Mene]

I can provide some clarification on the concept of causality in systems. In order for a system to be considered causal, it must meet two criteria: 1) the output at any given time is only dependent on present and past inputs, and 2) the output cannot be affected by future inputs. This means that the system cannot have any knowledge of future inputs or events in order to produce its output.

In the case of the system y(n) = x(n3), we can see that the output at any given time n is only dependent on the present and past input values, which are represented by n3. This means that the system does not have any knowledge of future inputs and therefore meets the first criteria for causality.

To further understand this concept, let's look at an example. If we input n = 2, the system will output y(2) = x(2^3) = x(8). This output is dependent on the present input of 2 and the past input of 8. If we were to input a future value of n = 4, the system would still output y(4) = x(4^3) = x(64), which is only dependent on the present and past inputs of 4 and 64, respectively. The future input of n = 4 does not change the output of y(2) = x(8), thus fulfilling the second criteria for causality.

In conclusion, based on the definition of causality and the behavior of the system y(n) = x(n3), we can say that this system is indeed causal. It only depends on present and past inputs and is not affected by future inputs. I hope this helps clarify the concept for you.