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their sum. (27Y(t) - 90) + (72Y(t)-60)) = 99Y(t)-150 | their sum. (27Y(t) - 90) + (72Y(t)-60)) = 99Y(t)-150 | ||
| − | Now we will multiply the original signals by the constants, take their sum, and then send them through the system. | + | Now we will multiply the original signals by the constants, take their sum, and then send them through the system. |
| + | If we end up with 99Y(t)-150, then the system must be linear. So, (9*1X) + (6*4X) = 33x. This gives 99Y(t) - 150. | ||
| + | Therefore the system is linear. | ||
</pre> | </pre> | ||
Revision as of 17:20, 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 Now we will multiply the original signals by the constants, take their sum, and then send them through the system. If we end up with 99Y(t)-150, then the system must be linear. So, (9*1X) + (6*4X) = 33x. This gives 99Y(t) - 150. Therefore the system is linear.
Non Linear System
SYSTEM: y =
