Difference between revisions of "3.A David Hartmann - Linear System ECE301Fall2008mboutin" - Rhea

Revision as of 14:17, 19 September 2008

Linear System

Given any two inputs

x_1(t) \,

x_2(t) \,

as well as their respective outputs

y_1(t) = F \left \{ x_1(t) \right \}

y_2(t) = F \left \{ x_2(t) \right \}

then to be a linear system,

\alpha y_1(t) + \beta y_2(t) = F \left \{ \alpha x_1(t) + \beta x_2(t) \right \}

for any scalar complex values $\alpha \,$ and $\beta \,$ .

@@ Line 1: / Line 1: @@
 == Part A: Understanding System's Properties ==
 '''Linear System'''
+Given any two inputs
 :<math>x_1(t) \,</math>
 :<math>x_2(t) \,</math>
 as well as their respective outputs
-:<math>y_1(t) = H \left \{ x_1(t) \right \} </math>
+:<math>y_1(t) = F \left \{ x_1(t) \right \} </math>
-:<math>y_2(t) = H \left \{ x_2(t) \right \} </math>
+:<math>y_2(t) = F \left \{ x_2(t) \right \} </math>
-then a linear system must satisfy
+then to be a linear system,
-:<math>\alpha y_1(t) + \beta y_2(t) = H \left \{ \alpha x_1(t) + \beta x_2(t) \right \} </math>
+:<math>\alpha y_1(t) + \beta y_2(t) = F \left \{ \alpha x_1(t) + \beta x_2(t) \right \} </math>
-for any [[scalar (mathematics)_ECE301Fall2008mboutin|scalar]] values <math>\alpha \,</math> and <math>\beta \,</math>.
+for any scalar complex values <math>\alpha \,</math> and <math>\beta \,</math>.