Which of the following is a non-causal system?

Concept:

A system is said to be causal if the system is dependent on the present or past inputs only but not on the future input.

A system is time-invariant if a time shift in the input signal results in an identical time shift in the output signal.

y(n) = x(n) and y(n-k) = x (n – k)

A system is said to be linear if it follows both superposition and homogeneity.

A system is said to be stable if it gives bounded output for bounded input.

Calculation:

1. ​y(t) = 2x(t) + dx(t)/dt; it is causal as the output is dependent on only present and past inputs.

2. y(t) = x(t) – x(t – 1); it is causal as the output is dependent on only present and past inputs.

3. y(t) = t x(t); it is causal as the output is dependent on only present inputs.

4. y(t) = x(t) + 2 x(3 – t); it is non-causal as the output is dependent on future inputs..