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Filtering Sampled Continuous-Time SignalsFiltering Sampled Continuous-Time Signals• Consider the system model as shown below• Suppose thatxt = – t Xe jt• We know that after sampling we have(6.34)xn xnT s Xe jnT s= = =Xe jˆ n(6.35)• The key relationship to connect the continuous-time and thediscrete-time quantities isˆ = T s= 2 --ffˆ= ---- = ˆ f sT s= -----------ˆ=2T s(6.36)• As long as the input analog frequency satisfies the samplingtheorem, i.e., T sor f f s 2, the output <strong>of</strong> the discrete-timesystem will bef s-----ˆ f2 sECE 2610 Signals and Systems 6–27
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