Linear system explanation is given the ppt presentation

Linear system

1. Linear system A system satisfies the principal of supper position and homogeneity is called linaer system. The system can be represented by set of linear equation. Y(t)= mx (t)

2. Time variant system Time variant system: The system’s output directly depends on time. Y(t)= tx (t) Time invariant system: The system’s output does not directly depend on time. Y(t)=ax(t)

3. Transfer function For linear time invariant system the transfer function is defined as the ratio of Laplace transfer of output to Laplace transform of input under the assumption that all initial condition are zero.

4. Characteristic of transfer function It relates output variable to input variable. It is the property of system itself. It does not provide the physical structure of the system. It is used to analysis and determine the response of the system under different input.

5. Steps to find transfer function Find the mathematical equation depending upon the physical law. Take Laplace transform transformation of the equations considering the initial condition zero. Find the output to input ratio.

6. Laplace transform of the equation

7. Laplace transform of the equation