(New page: ==System== y(t)=7x(t) ==Impulse Response==) |
(→CT Input) |
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y(t)=7x(t) | y(t)=7x(t) | ||
==Impulse Response== | ==Impulse Response== | ||
| + | y(d(t))=7(d(t)) | ||
| + | <br> | ||
| + | so the impulse response is 7d(t) | ||
| + | ==System function== | ||
| + | H(s) = <math> \int_{-\infty}^{\infty}7\delta(\tau)e^{-s\tau}d\tau</math> | ||
| + | <br> | ||
| + | <math>H(s)=7</math> | ||
| + | ==CT Input== | ||
| + | <math>x(t)=cos(3*pi*t)cos(6*pi*t)\!</math> | ||
| + | |||
| + | a2=6 | ||
| + | a3=6 | ||
| + | a9=6 | ||
| + | a10=6 | ||
| + | |||
| + | <br> | ||
| + | fundamental period = <math>2\pi/6</math> | ||
| + | |||
| + | ==Response to Input== | ||
| + | |||
| + | <math>y(t)=42e^{2jt} + 42e^{3jt}+ 42e^{9jt}+ 42e^{10jt}</math> | ||
Latest revision as of 10:24, 26 September 2008
System
y(t)=7x(t)
Impulse Response
y(d(t))=7(d(t))
so the impulse response is 7d(t)
System function
H(s) = $ \int_{-\infty}^{\infty}7\delta(\tau)e^{-s\tau}d\tau $
$ H(s)=7 $
CT Input
$ x(t)=cos(3*pi*t)cos(6*pi*t)\! $
a2=6 a3=6 a9=6 a10=6
fundamental period = $ 2\pi/6 $
Response to Input
$ y(t)=42e^{2jt} + 42e^{3jt}+ 42e^{9jt}+ 42e^{10jt} $
