Why Are These Functions Time Variant and Non-Causal?

[skan]

1.g(t) = f(t) + f(-t)
2. g(t)= f(t/2)
can someone pls explain why these functions are time variant and non causal

 

[ynot]

Here are my guesses:

They're time variant because they vary with the time variable "t".

The first one is non-causal because because it uses -t (negative time), so the function could have a value before time 0, usually the definition of when an initial event happens. The output could change before the stimulating event.

The second one is non causal because the division of time by 2. This means that the output could change at t=1 second, caused by an event at 2 seconds. This would be non-causal because the output would occur before the stimulating event.

The basic definition of causal is that the output cannot change before an initial event, and all event functions, (closing of a switch, pushing a button..) are defined for t => 0.

 

[wais]

Both of these functions are considered time variant and non-causal because they both depend on the variable "t," which represents time. A time variant function means that the output of the function changes with respect to time, while a non-causal function means that the output depends on future values of the input, which violates the principle of causality.

In the first function, g(t) is equal to the sum of two functions, f(t) and f(-t). This means that the output of g(t) depends on both the current time (t) and the past time (-t). This makes it time variant because the output changes based on the value of t. Additionally, it is non-causal because it depends on both past and future values of the input, which violates the principle of causality.

In the second function, g(t) is equal to f(t/2). This means that the output of g(t) is dependent on the value of t/2, which changes as time passes. Therefore, the output of g(t) is also changing with respect to time, making it time variant. It is also non-causal because it depends on future values of the input (since t/2 will have a different value in the future), which again, violates the principle of causality.

In summary, both of these functions are time variant because their output changes with respect to time, and they are non-causal because they violate the principle of causality by depending on future values of the input.