Difference between revisions of "HW2.C Jun Hyeong Park ECE301Fall2008mboutin" - Rhea

Latest revision as of 07:05, 6 September 2008

Linear system is a system that satisfies a principle of superpositon.

system T : y = 2x(t)

y1(t) = 2x1(t)
y2(t) = 2x2(t)
W(t) = 2x1(t) + 2x2(t)
Y(t) = 2(x1(t) + x2(t)) = 2x1(t) + 2x2(t)
W(t) = Y(t)

Therefore, this is linear system.

system H : y=2x(t) + 5

y1(t) = 2x1(t) + 5

y2(t) = 2x2(t) + 5

W(t) = 2x1(t) + 2x2(t) + 10

Y(t) = 2(x1(t) + x2(t)) + 5

W(t) != Y(t)

Therefore, this is Non-linear system.

@@ Line 1: / Line 1: @@
 == Linear system ==
-Linear system is a system that satisfies a principle of superpositon. For example, if sinusoid signal is input of a linear system, the frequency of output signal is not changed. Only amplitude and phase can be changed.
+Linear system is a system that satisfies a principle of superpositon.
 == Example of Linear system ==
-y1(t) = T{x1(t)}<br>
+system T : y = 2x(t)
-y2(t) = T(x2(t))<br>
-W(t) a*T{x1(t)} + a*T{x(2)}<br>
+y1(t) = 2x1(t) <br>
+y2(t) = 2x2(t) <br>
+W(t) = 2x1(t) + 2x2(t) <br>
+Y(t) = 2(x1(t) + x2(t)) = 2x1(t) + 2x2(t) <br>
+W(t) = Y(t) <br>
+Therefore, this is linear system.
+== Example of Non-linear system ==
+system H : y=2x(t) + 5
+y1(t) = 2x1(t) + 5
+y2(t) = 2x2(t) + 5
+W(t) = 2x1(t) + 2x2(t) + 10
+Y(t) = 2(x1(t) + x2(t)) + 5
+W(t) != Y(t)
-Y(t) = T{a*x1(t) + a*x2(t)}<br>
+Therefore, this is Non-linear system.
-If W(t) eaquals to Y(t), System T is linear system.
+== Example of non-linear system ==