What is a system?

• A signal was defined as a mapping from a set of the independent variable (domain) to the set of the dependent variable (co-domain).
• A system is also a mapping, but across signals, or across mappings .

Examples of systems

Examples of systems are all around us.

• The speakers that go with your computer can be looked at as systems whose input is voltage pulses from the CPU and output is music (audio signal).
• A spring may be looked as a system with the input , say, the longitudinal force on it as a function of time, and output signal being its elongation as a function of time

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. 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.

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.