(→Example of Non-Linear System) |
|||
| (3 intermediate revisions by the same user not shown) | |||
| Line 2: | Line 2: | ||
According to what I have understood, If a system input x(t) produces and output y(t), then it follows that if the system input is x(t+d) then output will be y(t+d). Also another idea is, If x1(t) --> y1(t) and x2(t) --> y2(t), then it follows that the input to the same system a1.x1(t)+a2.x2(t) gives output a1y1(t)+ a2y2(t) | According to what I have understood, If a system input x(t) produces and output y(t), then it follows that if the system input is x(t+d) then output will be y(t+d). Also another idea is, If x1(t) --> y1(t) and x2(t) --> y2(t), then it follows that the input to the same system a1.x1(t)+a2.x2(t) gives output a1y1(t)+ a2y2(t) | ||
==Example of a Linear System== | ==Example of a Linear System== | ||
| + | |||
| + | Given the system y(t) = 2x(t) | ||
| + | |||
| + | Input x1(t) = 4n and x2(t) = 10, we get y1(t) = 8n and y2(t) = 20. y1(t) + y2(t) = 8n+20 | ||
| + | |||
| + | Input sum of the two inputs x(t) = 4n + 10, we get output y3(t) = 8n+20. | ||
| + | |||
| + | So--> y1(t) + y2(t) = y3(t) the system is LINEAR. | ||
| + | |||
==Example of Non-Linear System== | ==Example of Non-Linear System== | ||
| + | GIVEN | ||
| + | |||
| + | x1(t) = t | ||
| + | |||
| + | x2(t) = t^2 | ||
| + | |||
| + | y(t) = sin(x) | ||
| + | |||
| + | y1(t) = sin(t) | ||
| + | |||
| + | y2(t) = sin(t^2) | ||
| + | |||
| + | ay1 + by2 = a*sin(t) + b*sin(t^2) != Sin(ax1+bx2) | ||
| + | |||
| + | So Non-Linear. | ||
Latest revision as of 16:03, 12 September 2008
Linear Systems
According to what I have understood, If a system input x(t) produces and output y(t), then it follows that if the system input is x(t+d) then output will be y(t+d). Also another idea is, If x1(t) --> y1(t) and x2(t) --> y2(t), then it follows that the input to the same system a1.x1(t)+a2.x2(t) gives output a1y1(t)+ a2y2(t)
Example of a Linear System
Given the system y(t) = 2x(t)
Input x1(t) = 4n and x2(t) = 10, we get y1(t) = 8n and y2(t) = 20. y1(t) + y2(t) = 8n+20
Input sum of the two inputs x(t) = 4n + 10, we get output y3(t) = 8n+20.
So--> y1(t) + y2(t) = y3(t) the system is LINEAR.
Example of Non-Linear System
GIVEN
x1(t) = t
x2(t) = t^2
y(t) = sin(x)
y1(t) = sin(t)
y2(t) = sin(t^2)
ay1 + by2 = a*sin(t) + b*sin(t^2) != Sin(ax1+bx2)
So Non-Linear.
