| Line 14: | Line 14: | ||
importance | importance | ||
| − | replacing a differentiation operation in the time domain with a multiplication operation in the frequecy domain | + | replacing a differentiation operation in the time domain with a multiplication operation in the frequecy domain for easier Fourier transform enalysis |
example | example | ||
| − | x(t) = | + | x(t)=u(t) |
<math>X(j*w)=G(j*w)*(1/jw)+\pi*G(0)*\delta(w)</math> | <math>X(j*w)=G(j*w)*(1/jw)+\pi*G(0)*\delta(w)</math> | ||
<math>X(j*w)=(1/(j*w))+\pi*G(0)*\delta(w)</math> | <math>X(j*w)=(1/(j*w))+\pi*G(0)*\delta(w)</math> | ||
Latest revision as of 04:45, 9 July 2009
Differentiation
def. x'(t) = j*w*(j*w)
x(t) = $ \int\limits_{-\infty}^{\infty}X(jw)e^{(-\jmath wt)}dt $
diffrentiate both sides
x'(t) = d($ \int\limits_{-\infty}^{\infty}X(jw)e^{(-\jmath wt)}dt $)
x'(t) = j*w*(j*w)
importance
replacing a differentiation operation in the time domain with a multiplication operation in the frequecy domain for easier Fourier transform enalysis
example
x(t)=u(t)
$ X(j*w)=G(j*w)*(1/jw)+\pi*G(0)*\delta(w) $
$ X(j*w)=(1/(j*w))+\pi*G(0)*\delta(w) $
