Overview
A system in Signal and Systems terminology is just a function from one signal to another.
{% H: x(t) \rightarrow y(t) %}
Here, there is no assumption whether the signals represent continuous time process, or discrete, or even if they are one-dimensional or
multi. In the language of formal mathematics, a system is just an
operator.
A system will often be written as
{% y(t) = H(x(t)) %}
That is, the output signal is the result of applying the function {% H %} to the signal {% x(t) %}.
This is not to be interpreted that {% y(t) %} is dependent only the value of the signal, {% x %} at {% t %}.
That is, {% y %} could a function of the value of {% x %} at every point {% t %} from the domain of the input signal.