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Introduction to Systems

2 June, 2016 - 15:17

Signals are manipulated by systems. Mathematically, we represent what a system does by the notation y (t)= S (x (t)), with x representing the input signal and y the output signal.

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Figure 2.9 Definition of a system
The system depicted has input x (t) and output y (t). Mathematically, systems operate on function(s) to produce other function(s). In many ways, systems are like functions, rules that yield a value for the dependent variable (our output signal) for each value of its independent variable (its input signal). The notation y (t)= S (x (t)) corresponds to this block diagram. We term S (·) the input-output relation for the  

This notation mimics the mathematical symbology of a function: A system's input is analogous to an independent variable and its output the dependent variable. For the mathematically inclined, a system is a functional: a function of a function (signals are functions).

Simple systems can be connected together one system's output becomes another's input to accomplish some overall design. Interconnection topologies can be quite complicated, but usually consist of weaves of three basic interconnection forms.