(Non Linear System)
(Linear system)
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such as 9 and 6.  Now multiply the output from "a" by 9.  Then multiply the output from "b" by 6.  Now take
 
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
 
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 it is linear.
 
</pre>
 
</pre>
 +
 
== Non Linear System ==
 
== Non Linear System ==
  
 
SYSTEM: y =
 
SYSTEM: y =

Revision as of 18:19, 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 it is linear.

Non Linear System

SYSTEM: y =

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