How do you find whether a system is invertible?

How do you find whether a system is invertible?

Invertibility and inverse systems: A system is called invertible if it produces distinct output signals for distinct input signals. If an invertible system produces the output ( ) for the input ( ), then its inverse produces the output ( ) for the input ( ):

What is non-invertible system?

A system is called non-invertible if there should be many to one mapping between input and output at a particular instant. Example : Determine whether or not each of the following systems are invertible with input x(t) and output y(t). Since different inputs leads to same output hence system is non-invertible.

Can a system have more than one inverse system?

Another query is that can a system has more than one inverse systems , sometime before I used to think that inverse pairs are unique but just solving an example of finding inverse of differentiation as LTI system i came to result that it has got two inverses

How to determine if a system is invertible?

Example 3.2 Determine if the following systems are invertible or not (a) (b) (c) (d) H. C. So Page 7 Semester B 2016-2017 (a) The system is invertible because we can pass using another system to produce .

Can a discrete time system be invertible?

Note that zeros on the imaginary axis (for continuous-time systems) or on the unit circle (for discrete-time systems) are not allowed. Sometimes such systems are called strictly minimum-phase. The differentiator mentioned in your question is an example of a system that cannot be inverted.

Can a causal and stable system be invertible?

If all zeros of the original system lie in the left half plane (for continuous-time systems), or inside the unit circle (for discrete-time systems), then the system is invertible, and its inverse system is causal and stable. Such systems are called minimum-phase systems. Minimum-phase systems can be inverted by causal and stable systems.