Linear time-invariant theory, commonly known as
LTI system theory, comes from
applied mathematics and has direct applications in
NMR spectroscopy,
seismology,
circuits,
signal processing,
control theory, and other technical areas. It investigates the response of a
linear and
time-invariant system to an arbitrary input signal. Trajectories of these systems are commonly measured and tracked as they move through time (e.g., an acoustic waveform), but in applications like
image processing and
field theory, the LTI systems also have trajectories in spatial dimensions. Thus, these systems are also called
linear translation-invariant to give the theory the most general reach. In the case of generic
discrete-time (i.e.,
sampled) systems,
linear shift-invariant is the corresponding term. A good example of LTI systems are electrical circuits that can be made up of resistors, capacitors, and inductors.