Page "Linear filter" Paragraph 46

LTI system theory describes linear time-invariant ( LTI ) filters of all types.

LTI filters can be completely described by their frequency response and phase response, the specification of which uniquely defines their impulse response, and vice versa.

From a mathematical viewpoint, continuous-time IIR LTI filters may be described in terms of linear differential equations, and their impulse responses considered as Green's functions of the equation.

Continuous-time LTI filters may also be described in terms of the Laplace transform of their impulse response, which allows all of the characteristics of the filter to be analyzed by considering the pattern of poles and zeros of their Laplace transform in the complex plane.

Similarly, discrete-time LTI filters may be analyzed via the Z-transform of their impulse response.