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*Fourier series coefficients 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 | ||
| − | :<math>x(t)=\sum_{n=-\infty}^\infty a_n e^{j \frac{2\pi}{T}nt}</math> | + | :<math>x(t)=\sum_{n=-\infty}^\infty a_n e^{j \frac{2\pi}{T}nt}</math> <math>a_n=\frac{1}{T} \int_{0}^T x(t) e^{-j \frac{2\pi}{T}nt}dt</math> |
| − | :<math>\ F(f) = \int_{-\infty}^{\infty} x(t)\ e^{- j 2 \pi f t}\,dt </math> | + | :<math>\ F(f) = \int_{-\infty}^{\infty} x(t)\ e^{- j 2 \pi f t}\,dt </math><text> </text><math>\ f(t) = \int_{-\infty}^{\infty} F(f)\ e^{j 2 \pi f t}\,df </math> |
Revision as of 04:41, 30 September 2010
Work in progress for a formula sheet?
- 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
- $ 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 $
- $ \ F(f) = \int_{-\infty}^{\infty} x(t)\ e^{- j 2 \pi f t}\,dt $<text> </text>$ \ f(t) = \int_{-\infty}^{\infty} F(f)\ e^{j 2 \pi f t}\,df $
