10/09 - Fourier Transform: Difference between revisions
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==Examples== | ==Examples== | ||
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|<math>\int_{-\infty}^{\infty}e^{j2\pi ft}e^{-j2\pi f\lambda}df</math> | |||
|<math>=\left\langle e^{j2\pi ft}\mid e^{j2\pi ft}\right\rangle_f</math> | |||
|<math>=\delta(t-\lambda)\,\!</math> | |||
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|<math>\int_{-\infty}^{\infty}e^{j2\pi tf}e^{-j2\pi tf_0}dt</math> | |||
|<math>=\left\langle e^{j2\pi tf}\mid e^{j2\pi tf_0}\right\rangle_t</math> | |||
|<math>=\delta(f-f_0)\,\!</math> | |||
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===Sifting property of the delta function=== | ===Sifting property of the delta function=== | ||
Revision as of 18:09, 17 November 2008
Assuming the function is perodic with the period T | ||
Fourier Transform
Remember from 10/02 - Fourier Series
If we let
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