Determine if each of the following systems is invertible

1. How do you know if a system is invertible?
2. What is invertible and non invertible system?
3. What is the inverse system in DSP?

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.)

What is invertible and non invertible system?

Definition (discrete-time): A system H is invertible if there exists a system Hinv with the property that HinvHx[n] = x[n] for any signal x[n]. Examples: Invertible: y[n] = x[n]+0.5x[n − 1]. Not invertible: y[n]=(x[n])2 .

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].