10/09 - Fourier Transform: Difference between revisions

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|<math>\rightarrow \int_{-\infty}^{\infty}() df</math>
|<math>\rightarrow \int_{-\infty}^{\infty}() df</math>
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==Definitions==
<math></math>

Revision as of 14:27, 17 November 2008

ej2πnt/Tej2πmt/T =ej2πnt/Tej2πmt/Tdt
=ej2π(nm)t/Tdt
=T/2T/2ej2π(nm)t/Tdt Assuming the function is perodic with the period T
=Tδm,n

Fourier Transform

Remember from 10/02 - Fourier Series

  • αm=1TT/2T/2x(t)ej2πmt/Tdt
  • x(t)=x(t+T)=n=αmej2πm/T

If we let T

1T df
nT f Remember f=2πnT
T
n=1T ()df

Definitions