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== Linear system == | == Linear system == | ||
SYSTEM: y = 3x(t) - 10 | SYSTEM: y = 3x(t) - 10 | ||
| − | 1X1(t) --> SYSTEM --> 3Y1(t) - 10 | + | a.) 1X1(t) --> SYSTEM --> 3Y1(t) - 10 |
| − | 4X2(t) --> SYSTEM --> 12Y2(t) - 10 | + | b.) 4X2(t) --> SYSTEM --> 12Y2(t) - 10 |
| + | |||
| + | We can do the following proof to show that the above system is linear. Take two random constant numbers such as 9 and 6. Now multiply the output from "a" by 9. Then multiply the output from "b" by 6. Now take their sum. (27Y(t) - 90) + (72Y(t)-60)) = 99Y(t)-150 | ||
An example of a linear system is shown below: | An example of a linear system is shown below: | ||
Revision as of 18:08, 10 September 2008
== Linear system == SYSTEM: y = 3x(t) - 10 a.) 1X1(t) --> SYSTEM --> 3Y1(t) - 10 b.) 4X2(t) --> SYSTEM --> 12Y2(t) - 10 We can do the following proof to show that the above system is linear. Take two random constant numbers such as 9 and 6. Now multiply the output from "a" by 9. Then multiply the output from "b" by 6. Now take their sum. (27Y(t) - 90) + (72Y(t)-60)) = 99Y(t)-150 An example of a linear system is shown below: x1(t) --> system --> y1(t) x2(t) --> system --> y2(t)
