m |
m |
||
| Line 1: | Line 1: | ||
| − | |||
=2010_Fall_ECE_438_Boutin/ECE438Mid1FormulaSheet_Work_wrk= | =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 | ||
| − | + | :<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(t) = \int_{-\infty}^{\infty} F(f)\ e^{j 2 \pi f t}\,df </math> | ||
[[ 2010 Fall ECE 438 Boutin/ECE438Mid1FormulaSheet Work|Back to 2010 Fall ECE 438 Boutin/ECE438Mid1FormulaSheet Work]] | [[ 2010 Fall ECE 438 Boutin/ECE438Mid1FormulaSheet Work|Back to 2010 Fall ECE 438 Boutin/ECE438Mid1FormulaSheet Work]] | ||
Revision as of 04:52, 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
- $ 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 $ $ \ f(t) = \int_{-\infty}^{\infty} F(f)\ e^{j 2 \pi f t}\,df $
Back to 2010 Fall ECE 438 Boutin/ECE438Mid1FormulaSheet Work
