The main idea is to explore the relationship between the blocked and the unblocked systems. These properties make LTI systems easy to represent and understand graphically. Time-invariant systems are systems where the output does not depend on when an input was applied. a) We shall first prove homogeneity and additivity imply linearity. Linear systems are systems whose outputs for a linear combination of inputs are the same as a linear combination of individual responses to those inputs. To say a system is linear is equivalent to saying the system obeys both additivity and homogeneity. scaling any input signal scales the output signal by the same factor. If an input $x_1(t)$ produces output $y_1(t)$ and another input $x_2(t)$ also acting along produces output $y_2(t)$, then, when both inputs acting on the system simultaneously, produces output $y_1(t) + y_2(t)$. This paper presents a systematic study on the properties of blocked linear systems that have resulted from blocking discrete-time linear time invariant systems. A system is said to be homogenous if, for any input signal X(t), i.e. It can be verified by either first law of homogeneity and law of additivity or by the two rules. Solution The function represents the conjugate of input. In this topic, you study the Linear and Nonlinear Systems theory, definition & solved examples.Ī system is called linear if it satisfies two properties Example 1 Check whether y ( t) x ( t) is linear or non-linear.