System description

The system description specifies the transformation of the input signal to the output signal. In certain cases, a system has a closed form description. E.g. the continuous-time system with description y(t) = x(t) + x(t-1); where x(t) is the input signal and y(t) is the output signal. Not all systems have such a closed form description. Just as certain "pathological" functions can only be specified by tabulating the value of the dependent variable against all values of the independent variable; some systems can only be described by tabulating the output signal against all possible input signals.

Explicit and Implicit Description

When a closed form system description is provided, it may either be classified as an explicit description or an implicit one.

For an explicit description, it is possible to express the output at a point, purely in terms of the input signal. Hence, when the input is known, it is easily possible to find the output of the system, when the system description is Explicit. In case of an Explicit description, it is clear to see the relationship between the input and the output. e.g. y(t) = { x(t) } ² + x(t-5).

In case the system has an Implicit description, it is harder to see the input-output relationship. An example of an Implicit description is y(t) - y(t-1) x(t) = 1. So when the input is provided, we are not directly able to calculate the output at that instant (since, the output at 't-1' also needs to be known). Although in this case also, there are methods to obtain the output based solely on the input, or, to convert this implicit description into an explicit one. The description by itself however is in the implicit form.