Invertible – Inverse Systems | Stable – Unstable Systems | Signals and Systems

A System is said to be invertible if the input of the system can be recovered from the system output. Alternatively, a system is said to be invertible if distinct inputs leads to distinct outputs. For example, if input is 5, output is 21. If input is 8, output is 29.

• If a system is invertible, inverse system exists
• Cascading of an invertible system & its inverse system is equivalent to the identity system
• The frequency response of an inverse system is basically reciprocal of the frequency response of the original system i.e., invertible system

STABLE & UNSTABLE SYSTEMS

A system is said to be BIBO (Bounded Input Bounded Output) stable if and only if every bounded input produces bounded output.

• Sine wave is bounded signal since its magnitude is always less than or equal to 1 (or peak amplitude).
• Output of a stable system does not diverge or does not grow unreasonably LARGE