linear time invariant system
A linear time invariant system (LTI) is a linear dynamical system ,
with parameter that is time independent. denotes the system output and denotes the input. The independent variable can be denoted as time, index for a discrete sequences or differential operaters (e.g. such as in Laplace domain or in frequency domain).
For example, for a simple mass-spring-dashpot system, the system parameter can be selected as the mass , spring constant and damping coefficient . The input to the said system can be chosen as the force applied to the mass and the output can be chosen as the mass’s displacement.
LTI system has the following properties.
If and , then
- Time Invariance:
If , then
A LTI system can be represented with the following:
Transfer function of Fourier transform variable , which is commonly used in communication theory and signal processing.
Transfer function of z-transform variable , which is commonly used in digital signal processing (DSP).
State-space equations, which is commonly used in modern control theory and mechanical systems.
Note that all transfer functions are LTI systems, but not all state-space equations are LTI systems.
|Title||linear time invariant system|
|Date of creation||2013-03-22 14:22:25|
|Last modified on||2013-03-22 14:22:25|
|Last modified by||Mathprof (13753)|