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| − | :<math>\ f(t) = \int_{-\infty}^{\infty} F(f)\ e^{j 2 \pi f t}\,df </math>..................... | + | :<math>CTFT</math><math>\ f(t) = \int_{-\infty}^{\infty} F(f)\ e^{j 2 \pi f t}\,df </math>.....................<math> \ F(f) = \int_{-\infty}^{\infty} x(t)\ e^{- j 2 \pi f t}\,dt</math> |
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Revision as of 06:00, 30 September 2010
2010_Fall_ECE_438_Boutin/ECE438Mid1FormulaSheet_Work_wrk
- Fourier series of a continuous-time signal x(t) periodic with period T
- Fourier series coefficients of a continuous-time signal x(t) periodic with period T
- $ DTFS $ $ x(t)=\sum_{n=-\infty}^\infty a_n e^{j \frac{2\pi}{T}nt} $ ...................... $ a_n=\frac{1}{T} \int_{0}^T x(t) e^{-j \frac{2\pi}{T}nt}dt $
- $ CTFT $$ \ f(t) = \int_{-\infty}^{\infty} F(f)\ e^{j 2 \pi f t}\,df $.....................$ \ F(f) = \int_{-\infty}^{\infty} x(t)\ e^{- j 2 \pi f t}\,dt $
$ comb_T [x(t)] \iff \frac{1}{T}rep_\frac{1}{T} [ \mathrm{X}(f)] $
$ rep_T [x(t)] \iff \frac{1}{T}comb_\frac{1}{T} [ \mathrm{X}(f)] $
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