A Linear Time Invariant (LTI) system is a type of mathematical model used in science and engineering to describe the behavior of a system over time. It is characterized by two properties: linearity and time-invariance.
A linear system follows the principle of superposition, which means that the output of the system is equal to the sum of the individual inputs. In other words, the response of the system to a combination of inputs is equal to the sum of the responses to each individual input.
A time-invariant system is one in which the output of the system does not change over time, regardless of when the input is applied. This means that the system's behavior is consistent and predictable, making it easier to analyze and understand.
Some common examples of LTI systems include electrical circuits, mechanical systems, and digital filters. These systems follow the principles of linearity and time-invariance and can be described using mathematical equations.
LTI systems are important because they provide a simplified and efficient way to model and analyze complex systems. By understanding the behavior of a linear time-invariant system, scientists and engineers can make predictions and design better solutions for real-world problems.