+ 
+ Introduction
+In this part we will learn to classify systems and recognize a Linear-Time Invariant System
+Let’s first define what a system is.
+Systems
+Our definition of a system will be:
+++An entity that processes a signal/a set of signals to yield another signal/set of signals.
+
The input, also called excitation, goes through the system and the system spits out an output, also called response.
+Interconnection
+We can have multiple systems.
+If they are in sequence, we call it a series connection. +We can also have parallel connection.
+ +Number of inputs and outputs
+Single Input Single Output +Single Input Multiple Output +Multiple Input Single Output +Multiple Input Multiple Output
+Linearity
+A system is said to be linear if a linear combination of inputs yields the same linear combination of the outputs to each individual input: +$$ +x_1(t) \to y_1(t) \newline +x_2(t) \to y_2(t) +$$
+$$ +a x_1(t) + b x_2(t) \to a y_1(t) + b y_2(t) \ | \ \text{Superposition principle} +$$
+Recall that, Superposition $=$ homogeneity + additivity.
+Homogeneity: +$$ +a x(t) \to a y(t) +$$
+Additivity: +$$ +x_1(t) + x_2(t) \to a y_1(t) y_2(t) +$$
+Time-invariance
+A system is said to be time-invariant if a time shift in the input signal results in the same time shift in the output signal: +$$ +x(t) \to y(t) \newline +x(t - t_0) \to y(t - t_0) +$$
+Example
+$$ +y(t) = (sin(t))x(t) +$$
+$$ +y(t - t_0) = (sin(t - t_0))x(t - t_0) \neq (sin(t))x(t - t_0) +$$
+Which means this function is time variant!
+BIBO-stability
+A system is BIBO-stable if a bounded input results in a bounded +output
+Causality
+A system is causal if the value of the output at the present +instant depends only on the present and past values of the input +(it does not depend on future values)
+Dynamic
+A system is instantaneous or memoryless if it’s output at a +certain time instant depends only on the input at the same time +instant (it does not depend on past or future values of the input)
+Dynamic otherwise.
+Invertible
+Invertible if observing one output we can determine (only) one +input
+LTI
+Both linear and time-invariant
+ +