In signal processing, a system is something that accepts one or more input signals to produce one or more output signals. Filters are one of the most commonly used systems in signal processing,  mostly for the purpose of suppressing or modifying some of the frequency components of a signal a signal to a particular end.

 

A system is said to be homogeneous if multiplying the input by a constant is equivalent to multiplying the output by the same constant.  A system is said to be additive if the output produced for the sum of its input signals is equivalent to the sum of the outputs produced for of each of the individual input signals.  A system is said to satisfy superposition if it is both homogeneous and additive.  A system that satisfies superposition is said to be a linear system.

 

A system is said to be relaxed if it is not still responding to a previous input.

 

A linear system can be characterized by one of its most popular representations: its impulse response, its step response, or its frequency response.

 

The impulse response of a system is the output response produced when a unit input is applied to a previously relaxed system.  The step response of a system is the output response produced when a unit step is applied to a previously relaxed system.  Since the unit step is the time integration of a unit impulse, it follows from the properties of linear systems, that the step response of a system can be obtained by integrating its impulse response.  The frequency response of a system can be obtained by taking the Fourier transform of its impulse response.