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7.+Sampling+and+Reconstruction

# 7.+Sampling+and+Reconstruction - 7 Sampling and...

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7. Sampling and Reconstruction 7.1. Sampling (7.1) 7.2. Reconstruction (7.2) 7.3. Sampling Theorem (7.1, 7.3)

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7.1. Sampling 7.1.1. Time-Domain Expression of Sampling A continuous-time signal is converted into a discrete-time signal by sampling. Sampling can be periodic or not. We consider periodic sampling only. It is expressed as x(n)=x c (t)| t=nT =x c (nT). (7.1) x c (t) is a continuous-time signal. x(n) is the corresponding discrete- time signal. T is the sampling interval. 7.1.2. Frequency-Domain Expression of Sampling Let x c (t) be a continuous-time signal, X c ( ) be the continuous- time Fourier transform of x c (t), x(n) be a discrete-time signal, and X( ) be the discrete-time Fourier transform of x(n). If x(n)=x c (nT), then
t x c (t) nT x(n) X c ( ) X( T) Figure 7.1. Spectral Relation in Sampling. 2 /T T A A/T . T m 2 X T 1 ) ( X m c  (7.2) Letting = T in (7.2), we obtain . m T 2 X T 1 ) T ( X m c  (7.3)

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X( T) is the discrete-time Fourier transform of x(n) expressed in . (7.3) shows that X( T) equals X c ( ) extended with period 2 /T and divided by T (figure 7.1).
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7.+Sampling+and+Reconstruction - 7 Sampling and...

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