Inverse system of a box function

1. What is inverse of a system?
2. What is the inverse system in DSP?
3. How do you find the inverse of an LTI system?

What is inverse of a system?

In words, the inverse system can be described as follows. The original system transforms an input signal u into an output signal y. This transformation depends on the initial state vector x(0) of the system at time 0. The inverse system retrieves u from y if a suitable initial state (0) is chosen.

What is the inverse system in DSP?

The system H2(z) is the inverse of H1(z) if y[n] = x[n]. This is equivalent to saying H1(z)H2(z)=1 or h1[n] ∗ h2[n] = δ[n].

How do you find the inverse of an LTI system?

Invertibility of LTI systems:

If an LTI system is invertible then it will have a LTI inverse system. This means that we have a continuous time LTI system with impulse response h(t) and its inverse system with impulse response h1(t) which results in an output equal to x(t).