INVERTIBILITY

Definition:

A system is said to be invertible if the input of the system can be recovered from the system output.

Mathematical Representation

Let y(t) be applied to a second C.T.system represented by the operator H-1 as shown in fig.(b).

Output of the system  = H-1{Hx(t)}

                                                = H-1 H{x(t)}

The operator H-1 is called as the inverse operator and the system is called as the inverse system.

If we want the output of second system to equal to the original input signal X(t),then it is necessary that

                                                H-1 * H = I

Where I denotes the identity operator.

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