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 \nbsp $ $ 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 $

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