(New page: Complex signals can represent circuits fairly accurately. Complex signals consist of a real component along with an imaginary component. The imaginary component is represented by the lette...) |
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if your an engineer, a letter i for the rest of the mathematics literal world. | if your an engineer, a letter i for the rest of the mathematics literal world. | ||
| − | <math> | + | j=<math>\sqrt{-1}</math> |
| + | |||
| + | |||
| + | '''<math>j^2=-1</math>''' | ||
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| + | |||
| + | An important conversion: | ||
| + | |||
| + | |||
| + | '''<math>x(t)=e^{j\omega t}</math>''' | ||
| + | |||
| + | '''<math>e^{j\omega t}= cos\omega t + jsin\omega t</math>''' | ||
| + | |||
| + | |||
| + | An example of a complex signal/system would be '''x = 10 + 12j''' | ||
| + | Complex signals can do a fairly good job of describing systems | ||
| + | involving circuits and springs! As you can see above in the "Important | ||
| + | conversion" '''<math>e^{j\omega t}</math>''' is essentially a complex | ||
| + | number that represents typically oscillating mathematical symbols. | ||
| + | |||
| + | What we care about is that by altering the '''<math>\omega</math>''' we | ||
| + | can represent periodic oscillating systems as well as damped and undamped, but | ||
| + | we really care about the periodic ones. | ||
| + | |||
| + | We can test to see if our function\signal is periodic by '''<math>{\omega/ 2\Pi = rational number!}</math>''' | ||
Latest revision as of 14:17, 5 September 2008
Complex signals can represent circuits fairly accurately. Complex signals consist of a real component along with an imaginary component. The imaginary component is represented by the letter j if your an engineer, a letter i for the rest of the mathematics literal world.
j=$ \sqrt{-1} $
$ j^2=-1 $
An important conversion:
$ x(t)=e^{j\omega t} $
$ e^{j\omega t}= cos\omega t + jsin\omega t $
An example of a complex signal/system would be x = 10 + 12j
Complex signals can do a fairly good job of describing systems
involving circuits and springs! As you can see above in the "Important
conversion" $ e^{j\omega t} $ is essentially a complex
number that represents typically oscillating mathematical symbols.
What we care about is that by altering the $ \omega $ we can represent periodic oscillating systems as well as damped and undamped, but we really care about the periodic ones.
We can test to see if our function\signal is periodic by $ {\omega/ 2\Pi = rational number!} $
