Table of Formulas 1.22 2003/07/16 07:56:33 GMT-5 2004/01/12 04:56:14.470 US/Central Anders Gjendemsjo gjendems@NO-SPAM.tele.ntnu.no Anders Gjendemsjo gjendems@NO-SPAM.tele.ntnu.no Analog Time-discrete Table Formulas Fourier Lists important formulas, both analog and time discrete. Analog Time Discrete Delta function Unit sample δ t 0 for t0, t δ t 1 δ n 1 n0 0 Unit step function Unit step function u t 1 t0 0 u n 1 n0 0 Angular frequency Angular frequency Ω 2 F ω 2 f Energy Ea t x t 2 Energy Ed n x n 2 Power Pa 1 T0 t T0 2 T0 2 x t 2 Power Pd 1 N n N1 N1 N 1 x n 2 Convol. y t τ x τ h t τ Convol. y n k x k h n k Fourier Transformation Discrete Time Fourier Transform X Ω t x t Ω t X ω n x n ω n Inverse Fourier Transform Inverse DTFT x t 1 2 Ω X ω Ω t x n 1 2 ω X ω ω n Fourier coeffecients Discrete Fourier Transform αk 1 T0 t 0 T0 x t k Ω0 t X k n 0 N1 x n 2 N k n Series expansion Inverse DFT x t k αk k Ω0 t x n 1 N k 0 N1 X k 2 N k n Parseval Parseval t T1 T0 x t 2 k 1 αk 2 1N k 0 N1 X k 2 n 0 N1 x n 2