(→Example of Linear System) |
(→Problem 4) |
||
| Line 4: | Line 4: | ||
:<math>x_2(t) </math> | :<math>x_2(t) </math> | ||
with respective outputs: | with respective outputs: | ||
| − | :<math>y_1(t) = H [ x_1(t) ] </math> | + | :<math>y_1(t) = H*[ x_1(t) ] </math> |
| − | :<math>y_2(t) = H [ x_2(t) ] </math> | + | :<math>y_2(t) = H*[ x_2(t) ] </math> |
will satisfy the equation | will satisfy the equation | ||
| − | :<math>\alpha y_1(t) + \beta y_2(t) = H [ \alpha x_1(t) + \beta x_2(t) ]</math> | + | :<math>\alpha y_1(t) + \beta y_2(t) = H*[ \alpha x_1(t) + \beta x_2(t) ]</math> |
for any <math>\alpha </math> and <math>\beta </math>. | for any <math>\alpha </math> and <math>\beta </math>. | ||
Revision as of 07:38, 12 September 2008
Problem 4
A linear is system is a system that given two valid inputs:
- $ x_1(t) $
- $ x_2(t) $
with respective outputs:
- $ y_1(t) = H*[ x_1(t) ] $
- $ y_2(t) = H*[ x_2(t) ] $
will satisfy the equation
- $ \alpha y_1(t) + \beta y_2(t) = H*[ \alpha x_1(t) + \beta x_2(t) ] $
for any $ \alpha $ and $ \beta $.
Example of Linear System
- $ x_1(t) = 4t $
- $ x_2(t) = 3t $
- $ H = 87 $
therefore
- $ y_1(t) = H*[ x_1(t) ] = 87*[4t] $
- $ y_2(t) = H*[ x_2(t) ] = 87*[3t] $
will satisfy the equation
- $ \alpha y_1(t) + \beta y_2(t) = H [ \alpha x_1(t) + \beta x_2(t) ] $
for any $ \alpha $ and $ \beta $.
