System

Inverse system of a system with integral

Inverse system of a system with integral
  1. What is inverse of a system?
  2. Is an integrator system invertible?
  3. What is the inverse system in DSP?
  4. How do you know if a system is invertible?

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.

Is an integrator system invertible?

If a system T is invertible, will be T−1 invertible? The answer is no. For example, integrator and the derivative systems.

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 know if 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 ( ): Examples of invertible systems: ( = 0 below.)

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