Classification of systems
Systems are classified into the following categories: Liner and Non-liner Systems Time Variant and Time Invariant Systems Liner Time variant and Liner Time invariant systems Static and Dynamic Systems Causal and Non-causal Systems Invertible and Non-Invertible Systems Stable and Unstable Systems Liner and Non-liner Systems A system is said to be linear when it satisfies superposition and homogenate principles. Consider two systems with inputs as x 1 (t), x 2 (t), and outputs as y 1 (t), y 2 (t) respectively. Then, according to the superposition and homogenate principles, T [a 1 x 1 (t) + a 2 x 2 (t)] = a 1 T[x 1 (t)] + a 2 T[x 2 (t)] ∴ , T [a 1 x 1 (t) + a 2 x 2 (t)] = a 1 y 1 (t) + a 2 y 2 (t) From the above expression, is clear that response of overall system is equal to response of individual system. Example: (t) = x 2 (t) Solution: y 1 (t) = T[x 1 (t)] = x 1 2 (t) y 2 (t) = T[x 2 (t)] =...