# Summary4 - 3 Sampling Theorem If the highest frequency...

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Summary 4 Hamid Jafarkhani Digital Signal Processing Summary 4 – p. 1/ 3

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Sampling Sampling Period: T x [ n ] = x a ( nT ) Sampling rate: F s = 1 T Uniform sampling of a continuous-time sinusoid x a ( t ) = A cos(2 πFt + θ ) results in x [ n ] = A cos(2 πfn + θ ) , where f = FT For a continuous-time sinusoid that is sampled at a rate F s to give a discrete-time sinusoid with a frequency range - 1 2 f 1 2 so that the discrete-time sinusoid is unique, we require - F s 2 F F s 2 . Summary 4 – p. 2/
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Unformatted text preview: 3 Sampling Theorem If the highest frequency component in a continuous-time signal x a ( t ) is F max = B and the signal is sampled at a rate F s > 2 F max , then x a ( t ) can be recovered exactly from its samples x [ n ] using sinc interpolation : x a ( t ) = ∞ s-∞ x [ n ] g p t-n F s P where g ( t ) = sin(2 πBt ) 2 πBt Summary 4 – p. 3/ 3...
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Summary4 - 3 Sampling Theorem If the highest frequency...

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