(Example)
(Example)
Line 4: Line 4:
 
=<math>Y(jw)=H(jw)X(jw),  H(jw)=\frac{Y(jw)}{X(jw)}</math>
 
=<math>Y(jw)=H(jw)X(jw),  H(jw)=\frac{Y(jw)}{X(jw)}</math>
 
== Example ==
 
== Example ==
 
+
Consider a LTI system that is chracterized by the differential equation.
 
<math> \frac{d^2y(t)}{dt^2}+4\frac{dy(t)}{dt}+3y(t) = \frac{dx(t)}{dt}+2x(t)</math>
 
<math> \frac{d^2y(t)}{dt^2}+4\frac{dy(t)}{dt}+3y(t) = \frac{dx(t)}{dt}+2x(t)</math>
 +
 +
 +
 
<math> H(jw)=\frac{(jw)+2}{(jw)^2+4(jw)+3}</math>
 
<math> H(jw)=\frac{(jw)+2}{(jw)^2+4(jw)+3}</math>

Revision as of 16:33, 24 October 2008

System Characterized By Linear Constant-Coefficient Differential Equations

$ \sum_{k=0}^{N}a_k\frac {d^ky(t)}{dt^k} = \sum_{k=0}^{M}b_k\frac {d^kx(t)}{dt^k} $

=$ Y(jw)=H(jw)X(jw), H(jw)=\frac{Y(jw)}{X(jw)} $

Example

Consider a LTI system that is chracterized by the differential equation. $ \frac{d^2y(t)}{dt^2}+4\frac{dy(t)}{dt}+3y(t) = \frac{dx(t)}{dt}+2x(t) $


$ H(jw)=\frac{(jw)+2}{(jw)^2+4(jw)+3} $

Alumni Liaison

Correspondence Chess Grandmaster and Purdue Alumni

Prof. Dan Fleetwood