formulas - Discrete-time Fourier series x[n = k= N ak...

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Discrete-time Fourier series x [ n ] = X k = h N i a k e jk (2 π/N ) n (1) a k = 1 N X n = h N i x [ n ] e - jk (2 π/N ) n (2) Continuous-time Fourier series x ( t ) = X k = -∞ a k e jk (2 π/T ) t (3) a k = 1 T Z T x ( t ) e - jk (2 π/T ) t dt (4) Continuous-time Fourier transform x ( t ) = 1 2 π Z -∞ X ( ) e jωt (5) X ( ) = Z -∞ x ( t ) e - jωt dt (6) Discrete-time Fourier transform x [ n ] = 1 2 π Z 2 π X ( ) e jωn (7) X ( e ) = X n = -∞ x [ n ] e - jωn
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